springsuite: planemo/lib/python3.7/site-packages/networkx/algorithms/similarity.py annotate

author	guerler
date	Fri, 31 Jul 2020 00:32:28 -0400
parents
children

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1 56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	1 # -- coding: utf-8 --
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	2 # Copyright (C) 2010 by
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	3 # Aric Hagberg <hagberg@lanl.gov>
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	4 # Dan Schult <dschult@colgate.edu>
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	5 # Pieter Swart <swart@lanl.gov>
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	6 # All rights reserved.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	7 # BSD license.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	8 #
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	9 # Author: Andrey Paramonov <paramon@acdlabs.ru>
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	10 """ Functions measuring similarity using graph edit distance.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	11
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	12 The graph edit distance is the number of edge/node changes needed
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	13 to make two graphs isomorphic.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	14
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	15 The default algorithm/implementation is sub-optimal for some graphs.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	16 The problem of finding the exact Graph Edit Distance (GED) is NP-hard
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	17 so it is often slow. If the simple interface `graph_edit_distance`
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	18 takes too long for your graph, try `optimize_graph_edit_distance`
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	19 and/or `optimize_edit_paths`.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	20
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	21 At the same time, I encourage capable people to investigate
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	22 alternative GED algorithms, in order to improve the choices available.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	23 """
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	24 from itertools import product
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	25 import math
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	26 import networkx as nx
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	27 from operator import *
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	28 import sys
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	29
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	30 __author__ = 'Andrey Paramonov <paramon@acdlabs.ru>'
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	31
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	32 __all__ = [
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	33 'graph_edit_distance',
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	34 'optimal_edit_paths',
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	35 'optimize_graph_edit_distance',
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	36 'optimize_edit_paths',
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	37 'simrank_similarity',
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	38 'simrank_similarity_numpy',
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	39 ]
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	40
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	41
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	42 def debug_print(args, *kwargs):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	43 print(args, *kwargs)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	44
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	45
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	46 def graph_edit_distance(G1, G2, node_match=None, edge_match=None,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	47 node_subst_cost=None, node_del_cost=None,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	48 node_ins_cost=None,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	49 edge_subst_cost=None, edge_del_cost=None,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	50 edge_ins_cost=None,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	51 upper_bound=None):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	52 """Returns GED (graph edit distance) between graphs G1 and G2.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	53
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	54 Graph edit distance is a graph similarity measure analogous to
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	55 Levenshtein distance for strings. It is defined as minimum cost
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	56 of edit path (sequence of node and edge edit operations)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	57 transforming graph G1 to graph isomorphic to G2.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	58
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	59 Parameters
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	60 ----------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	61 G1, G2: graphs
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	62 The two graphs G1 and G2 must be of the same type.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	63
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	64 node_match : callable
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	65 A function that returns True if node n1 in G1 and n2 in G2
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	66 should be considered equal during matching.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	67
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	68 The function will be called like
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	69
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	70 node_match(G1.nodes[n1], G2.nodes[n2]).
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	71
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	72 That is, the function will receive the node attribute
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	73 dictionaries for n1 and n2 as inputs.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	74
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	75 Ignored if node_subst_cost is specified. If neither
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	76 node_match nor node_subst_cost are specified then node
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	77 attributes are not considered.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	78
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	79 edge_match : callable
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	80 A function that returns True if the edge attribute dictionaries
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	81 for the pair of nodes (u1, v1) in G1 and (u2, v2) in G2 should
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	82 be considered equal during matching.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	83
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	84 The function will be called like
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	85
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	86 edge_match(G1[u1][v1], G2[u2][v2]).
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	87
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	88 That is, the function will receive the edge attribute
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	89 dictionaries of the edges under consideration.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	90
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	91 Ignored if edge_subst_cost is specified. If neither
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	92 edge_match nor edge_subst_cost are specified then edge
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	93 attributes are not considered.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	94
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	95 node_subst_cost, node_del_cost, node_ins_cost : callable
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	96 Functions that return the costs of node substitution, node
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	97 deletion, and node insertion, respectively.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	98
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	99 The functions will be called like
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	100
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	101 node_subst_cost(G1.nodes[n1], G2.nodes[n2]),
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	102 node_del_cost(G1.nodes[n1]),
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	103 node_ins_cost(G2.nodes[n2]).
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	104
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	105 That is, the functions will receive the node attribute
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	106 dictionaries as inputs. The functions are expected to return
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	107 positive numeric values.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	108
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	109 Function node_subst_cost overrides node_match if specified.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	110 If neither node_match nor node_subst_cost are specified then
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	111 default node substitution cost of 0 is used (node attributes
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	112 are not considered during matching).
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	113
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	114 If node_del_cost is not specified then default node deletion
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	115 cost of 1 is used. If node_ins_cost is not specified then
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	116 default node insertion cost of 1 is used.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	117
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	118 edge_subst_cost, edge_del_cost, edge_ins_cost : callable
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	119 Functions that return the costs of edge substitution, edge
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	120 deletion, and edge insertion, respectively.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	121
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	122 The functions will be called like
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	123
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	124 edge_subst_cost(G1[u1][v1], G2[u2][v2]),
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	125 edge_del_cost(G1[u1][v1]),
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	126 edge_ins_cost(G2[u2][v2]).
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	127
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	128 That is, the functions will receive the edge attribute
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	129 dictionaries as inputs. The functions are expected to return
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	130 positive numeric values.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	131
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	132 Function edge_subst_cost overrides edge_match if specified.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	133 If neither edge_match nor edge_subst_cost are specified then
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	134 default edge substitution cost of 0 is used (edge attributes
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	135 are not considered during matching).
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	136
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	137 If edge_del_cost is not specified then default edge deletion
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	138 cost of 1 is used. If edge_ins_cost is not specified then
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	139 default edge insertion cost of 1 is used.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	140
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	141 upper_bound : numeric
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	142 Maximum edit distance to consider. Return None if no edit
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	143 distance under or equal to upper_bound exists.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	144
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	145 Examples
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	146 --------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	147 >>> G1 = nx.cycle_graph(6)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	148 >>> G2 = nx.wheel_graph(7)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	149 >>> nx.graph_edit_distance(G1, G2)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	150 7.0
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	151
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	152 See Also
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	153 --------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	154 optimal_edit_paths, optimize_graph_edit_distance,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	155
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	156 is_isomorphic (test for graph edit distance of 0)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	157
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	158 References
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	159 ----------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	160 .. [1] Zeina Abu-Aisheh, Romain Raveaux, Jean-Yves Ramel, Patrick
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	161 Martineau. An Exact Graph Edit Distance Algorithm for Solving
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	162 Pattern Recognition Problems. 4th International Conference on
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	163 Pattern Recognition Applications and Methods 2015, Jan 2015,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	164 Lisbon, Portugal. 2015,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	165 <10.5220/0005209202710278>. <hal-01168816>
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	166 https://hal.archives-ouvertes.fr/hal-01168816
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	167
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	168 """
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	169 bestcost = None
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	170 for vertex_path, edge_path, cost in \
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	171 optimize_edit_paths(G1, G2, node_match, edge_match,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	172 node_subst_cost, node_del_cost, node_ins_cost,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	173 edge_subst_cost, edge_del_cost, edge_ins_cost,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	174 upper_bound, True):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	175 #assert bestcost is None or cost < bestcost
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	176 bestcost = cost
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	177 return bestcost
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	178
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	179
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	180 def optimal_edit_paths(G1, G2, node_match=None, edge_match=None,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	181 node_subst_cost=None, node_del_cost=None,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	182 node_ins_cost=None,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	183 edge_subst_cost=None, edge_del_cost=None,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	184 edge_ins_cost=None,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	185 upper_bound=None):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	186 """Returns all minimum-cost edit paths transforming G1 to G2.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	187
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	188 Graph edit path is a sequence of node and edge edit operations
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	189 transforming graph G1 to graph isomorphic to G2. Edit operations
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	190 include substitutions, deletions, and insertions.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	191
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	192 Parameters
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	193 ----------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	194 G1, G2: graphs
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	195 The two graphs G1 and G2 must be of the same type.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	196
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	197 node_match : callable
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	198 A function that returns True if node n1 in G1 and n2 in G2
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	199 should be considered equal during matching.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	200
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	201 The function will be called like
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	202
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	203 node_match(G1.nodes[n1], G2.nodes[n2]).
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	204
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	205 That is, the function will receive the node attribute
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	206 dictionaries for n1 and n2 as inputs.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	207
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	208 Ignored if node_subst_cost is specified. If neither
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	209 node_match nor node_subst_cost are specified then node
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	210 attributes are not considered.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	211
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	212 edge_match : callable
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	213 A function that returns True if the edge attribute dictionaries
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	214 for the pair of nodes (u1, v1) in G1 and (u2, v2) in G2 should
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	215 be considered equal during matching.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	216
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	217 The function will be called like
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	218
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	219 edge_match(G1[u1][v1], G2[u2][v2]).
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	220
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	221 That is, the function will receive the edge attribute
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	222 dictionaries of the edges under consideration.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	223
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	224 Ignored if edge_subst_cost is specified. If neither
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	225 edge_match nor edge_subst_cost are specified then edge
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	226 attributes are not considered.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	227
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	228 node_subst_cost, node_del_cost, node_ins_cost : callable
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	229 Functions that return the costs of node substitution, node
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	230 deletion, and node insertion, respectively.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	231
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	232 The functions will be called like
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	233
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	234 node_subst_cost(G1.nodes[n1], G2.nodes[n2]),
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	235 node_del_cost(G1.nodes[n1]),
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	236 node_ins_cost(G2.nodes[n2]).
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	237
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	238 That is, the functions will receive the node attribute
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	239 dictionaries as inputs. The functions are expected to return
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	240 positive numeric values.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	241
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	242 Function node_subst_cost overrides node_match if specified.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	243 If neither node_match nor node_subst_cost are specified then
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	244 default node substitution cost of 0 is used (node attributes
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	245 are not considered during matching).
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	246
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	247 If node_del_cost is not specified then default node deletion
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	248 cost of 1 is used. If node_ins_cost is not specified then
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	249 default node insertion cost of 1 is used.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	250
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	251 edge_subst_cost, edge_del_cost, edge_ins_cost : callable
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	252 Functions that return the costs of edge substitution, edge
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	253 deletion, and edge insertion, respectively.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	254
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	255 The functions will be called like
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	256
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	257 edge_subst_cost(G1[u1][v1], G2[u2][v2]),
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	258 edge_del_cost(G1[u1][v1]),
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	259 edge_ins_cost(G2[u2][v2]).
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	260
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	261 That is, the functions will receive the edge attribute
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	262 dictionaries as inputs. The functions are expected to return
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	263 positive numeric values.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	264
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	265 Function edge_subst_cost overrides edge_match if specified.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	266 If neither edge_match nor edge_subst_cost are specified then
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	267 default edge substitution cost of 0 is used (edge attributes
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	268 are not considered during matching).
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	269
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	270 If edge_del_cost is not specified then default edge deletion
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	271 cost of 1 is used. If edge_ins_cost is not specified then
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	272 default edge insertion cost of 1 is used.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	273
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	274 upper_bound : numeric
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	275 Maximum edit distance to consider.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	276
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	277 Returns
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	278 -------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	279 edit_paths : list of tuples (node_edit_path, edge_edit_path)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	280 node_edit_path : list of tuples (u, v)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	281 edge_edit_path : list of tuples ((u1, v1), (u2, v2))
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	282
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	283 cost : numeric
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	284 Optimal edit path cost (graph edit distance).
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	285
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	286 Examples
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	287 --------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	288 >>> G1 = nx.cycle_graph(6)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	289 >>> G2 = nx.wheel_graph(7)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	290 >>> paths, cost = nx.optimal_edit_paths(G1, G2)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	291 >>> len(paths)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	292 84
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	293 >>> cost
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	294 7.0
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	295
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	296 See Also
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	297 --------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	298 graph_edit_distance, optimize_edit_paths
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	299
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	300 References
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	301 ----------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	302 .. [1] Zeina Abu-Aisheh, Romain Raveaux, Jean-Yves Ramel, Patrick
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	303 Martineau. An Exact Graph Edit Distance Algorithm for Solving
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	304 Pattern Recognition Problems. 4th International Conference on
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	305 Pattern Recognition Applications and Methods 2015, Jan 2015,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	306 Lisbon, Portugal. 2015,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	307 <10.5220/0005209202710278>. <hal-01168816>
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	308 https://hal.archives-ouvertes.fr/hal-01168816
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	309
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	310 """
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	311 paths = list()
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	312 bestcost = None
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	313 for vertex_path, edge_path, cost in \
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	314 optimize_edit_paths(G1, G2, node_match, edge_match,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	315 node_subst_cost, node_del_cost, node_ins_cost,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	316 edge_subst_cost, edge_del_cost, edge_ins_cost,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	317 upper_bound, False):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	318 #assert bestcost is None or cost <= bestcost
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	319 if bestcost is not None and cost < bestcost:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	320 paths = list()
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	321 paths.append((vertex_path, edge_path))
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	322 bestcost = cost
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	323 return paths, bestcost
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	324
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	325
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	326 def optimize_graph_edit_distance(G1, G2, node_match=None, edge_match=None,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	327 node_subst_cost=None, node_del_cost=None,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	328 node_ins_cost=None,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	329 edge_subst_cost=None, edge_del_cost=None,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	330 edge_ins_cost=None,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	331 upper_bound=None):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	332 """Returns consecutive approximations of GED (graph edit distance)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	333 between graphs G1 and G2.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	334
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	335 Graph edit distance is a graph similarity measure analogous to
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	336 Levenshtein distance for strings. It is defined as minimum cost
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	337 of edit path (sequence of node and edge edit operations)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	338 transforming graph G1 to graph isomorphic to G2.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	339
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	340 Parameters
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	341 ----------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	342 G1, G2: graphs
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	343 The two graphs G1 and G2 must be of the same type.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	344
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	345 node_match : callable
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	346 A function that returns True if node n1 in G1 and n2 in G2
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	347 should be considered equal during matching.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	348
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	349 The function will be called like
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	350
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	351 node_match(G1.nodes[n1], G2.nodes[n2]).
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	352
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	353 That is, the function will receive the node attribute
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	354 dictionaries for n1 and n2 as inputs.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	355
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	356 Ignored if node_subst_cost is specified. If neither
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	357 node_match nor node_subst_cost are specified then node
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	358 attributes are not considered.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	359
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	360 edge_match : callable
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	361 A function that returns True if the edge attribute dictionaries
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	362 for the pair of nodes (u1, v1) in G1 and (u2, v2) in G2 should
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	363 be considered equal during matching.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	364
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	365 The function will be called like
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	366
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	367 edge_match(G1[u1][v1], G2[u2][v2]).
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	368
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	369 That is, the function will receive the edge attribute
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	370 dictionaries of the edges under consideration.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	371
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	372 Ignored if edge_subst_cost is specified. If neither
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	373 edge_match nor edge_subst_cost are specified then edge
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	374 attributes are not considered.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	375
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	376 node_subst_cost, node_del_cost, node_ins_cost : callable
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	377 Functions that return the costs of node substitution, node
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	378 deletion, and node insertion, respectively.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	379
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	380 The functions will be called like
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	381
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	382 node_subst_cost(G1.nodes[n1], G2.nodes[n2]),
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	383 node_del_cost(G1.nodes[n1]),
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	384 node_ins_cost(G2.nodes[n2]).
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	385
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	386 That is, the functions will receive the node attribute
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	387 dictionaries as inputs. The functions are expected to return
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	388 positive numeric values.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	389
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	390 Function node_subst_cost overrides node_match if specified.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	391 If neither node_match nor node_subst_cost are specified then
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	392 default node substitution cost of 0 is used (node attributes
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	393 are not considered during matching).
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	394
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	395 If node_del_cost is not specified then default node deletion
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	396 cost of 1 is used. If node_ins_cost is not specified then
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	397 default node insertion cost of 1 is used.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	398
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	399 edge_subst_cost, edge_del_cost, edge_ins_cost : callable
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	400 Functions that return the costs of edge substitution, edge
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	401 deletion, and edge insertion, respectively.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	402
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	403 The functions will be called like
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	404
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	405 edge_subst_cost(G1[u1][v1], G2[u2][v2]),
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	406 edge_del_cost(G1[u1][v1]),
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	407 edge_ins_cost(G2[u2][v2]).
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	408
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	409 That is, the functions will receive the edge attribute
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	410 dictionaries as inputs. The functions are expected to return
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	411 positive numeric values.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	412
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	413 Function edge_subst_cost overrides edge_match if specified.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	414 If neither edge_match nor edge_subst_cost are specified then
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	415 default edge substitution cost of 0 is used (edge attributes
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	416 are not considered during matching).
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	417
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	418 If edge_del_cost is not specified then default edge deletion
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	419 cost of 1 is used. If edge_ins_cost is not specified then
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	420 default edge insertion cost of 1 is used.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	421
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	422 upper_bound : numeric
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	423 Maximum edit distance to consider.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	424
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	425 Returns
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	426 -------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	427 Generator of consecutive approximations of graph edit distance.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	428
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	429 Examples
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	430 --------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	431 >>> G1 = nx.cycle_graph(6)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	432 >>> G2 = nx.wheel_graph(7)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	433 >>> for v in nx.optimize_graph_edit_distance(G1, G2):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	434 ... minv = v
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	435 >>> minv
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	436 7.0
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	437
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	438 See Also
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	439 --------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	440 graph_edit_distance, optimize_edit_paths
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	441
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	442 References
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	443 ----------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	444 .. [1] Zeina Abu-Aisheh, Romain Raveaux, Jean-Yves Ramel, Patrick
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	445 Martineau. An Exact Graph Edit Distance Algorithm for Solving
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	446 Pattern Recognition Problems. 4th International Conference on
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	447 Pattern Recognition Applications and Methods 2015, Jan 2015,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	448 Lisbon, Portugal. 2015,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	449 <10.5220/0005209202710278>. <hal-01168816>
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	450 https://hal.archives-ouvertes.fr/hal-01168816
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	451 """
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	452 for vertex_path, edge_path, cost in \
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	453 optimize_edit_paths(G1, G2, node_match, edge_match,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	454 node_subst_cost, node_del_cost, node_ins_cost,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	455 edge_subst_cost, edge_del_cost, edge_ins_cost,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	456 upper_bound, True):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	457 yield cost
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	458
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	459
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	460 def optimize_edit_paths(G1, G2, node_match=None, edge_match=None,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	461 node_subst_cost=None, node_del_cost=None,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	462 node_ins_cost=None,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	463 edge_subst_cost=None, edge_del_cost=None,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	464 edge_ins_cost=None,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	465 upper_bound=None, strictly_decreasing=True):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	466 """GED (graph edit distance) calculation: advanced interface.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	467
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	468 Graph edit path is a sequence of node and edge edit operations
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	469 transforming graph G1 to graph isomorphic to G2. Edit operations
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	470 include substitutions, deletions, and insertions.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	471
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	472 Graph edit distance is defined as minimum cost of edit path.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	473
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	474 Parameters
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	475 ----------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	476 G1, G2: graphs
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	477 The two graphs G1 and G2 must be of the same type.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	478
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	479 node_match : callable
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	480 A function that returns True if node n1 in G1 and n2 in G2
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	481 should be considered equal during matching.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	482
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	483 The function will be called like
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	484
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	485 node_match(G1.nodes[n1], G2.nodes[n2]).
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	486
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	487 That is, the function will receive the node attribute
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	488 dictionaries for n1 and n2 as inputs.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	489
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	490 Ignored if node_subst_cost is specified. If neither
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	491 node_match nor node_subst_cost are specified then node
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	492 attributes are not considered.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	493
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	494 edge_match : callable
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	495 A function that returns True if the edge attribute dictionaries
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	496 for the pair of nodes (u1, v1) in G1 and (u2, v2) in G2 should
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	497 be considered equal during matching.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	498
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	499 The function will be called like
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1" guerler parents: diff changeset	500

1

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1 # -*- coding: utf-8 -*-

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3 # Aric Hagberg <hagberg@lanl.gov>

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4 # Dan Schult <dschult@colgate.edu>

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5 # Pieter Swart <swart@lanl.gov>

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7 # BSD license.

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8 #

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9 # Author: Andrey Paramonov <paramon@acdlabs.ru>

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10 """ Functions measuring similarity using graph edit distance.

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11

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12 The graph edit distance is the number of edge/node changes needed

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13 to make two graphs isomorphic.

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14

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15 The default algorithm/implementation is sub-optimal for some graphs.

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16 The problem of finding the exact Graph Edit Distance (GED) is NP-hard

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17 so it is often slow. If the simple interface `graph_edit_distance`

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18 takes too long for your graph, try `optimize_graph_edit_distance`

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19 and/or `optimize_edit_paths`.

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20

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21 At the same time, I encourage capable people to investigate

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22 alternative GED algorithms, in order to improve the choices available.

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23 """

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24 from itertools import product

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25 import math

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26 import networkx as nx

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27 from operator import *

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28 import sys

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29

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30 __author__ = 'Andrey Paramonov <paramon@acdlabs.ru>'

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31

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32 __all__ = [

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33 'graph_edit_distance',

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34 'optimal_edit_paths',

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35 'optimize_graph_edit_distance',

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36 'optimize_edit_paths',

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37 'simrank_similarity',

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38 'simrank_similarity_numpy',

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39 ]

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40

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41

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42 def debug_print(*args, **kwargs):

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43 print(*args, **kwargs)

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44

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45

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46 def graph_edit_distance(G1, G2, node_match=None, edge_match=None,

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47 node_subst_cost=None, node_del_cost=None,

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48 node_ins_cost=None,

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49 edge_subst_cost=None, edge_del_cost=None,

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50 edge_ins_cost=None,

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51 upper_bound=None):

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52 """Returns GED (graph edit distance) between graphs G1 and G2.

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53

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54 Graph edit distance is a graph similarity measure analogous to

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55 Levenshtein distance for strings. It is defined as minimum cost

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56 of edit path (sequence of node and edge edit operations)

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57 transforming graph G1 to graph isomorphic to G2.

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58

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59 Parameters

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60 ----------

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61 G1, G2: graphs

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62 The two graphs G1 and G2 must be of the same type.

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63

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64 node_match : callable

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65 A function that returns True if node n1 in G1 and n2 in G2

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66 should be considered equal during matching.

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67

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68 The function will be called like

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69

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70 node_match(G1.nodes[n1], G2.nodes[n2]).

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71

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72 That is, the function will receive the node attribute

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73 dictionaries for n1 and n2 as inputs.

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74

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75 Ignored if node_subst_cost is specified. If neither

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76 node_match nor node_subst_cost are specified then node

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77 attributes are not considered.

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78

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79 edge_match : callable

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80 A function that returns True if the edge attribute dictionaries

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81 for the pair of nodes (u1, v1) in G1 and (u2, v2) in G2 should

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82 be considered equal during matching.

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83

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84 The function will be called like

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85

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86 edge_match(G1[u1][v1], G2[u2][v2]).

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87

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88 That is, the function will receive the edge attribute

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89 dictionaries of the edges under consideration.

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90

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91 Ignored if edge_subst_cost is specified. If neither

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92 edge_match nor edge_subst_cost are specified then edge

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93 attributes are not considered.

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94

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95 node_subst_cost, node_del_cost, node_ins_cost : callable

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96 Functions that return the costs of node substitution, node

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97 deletion, and node insertion, respectively.

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98

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99 The functions will be called like

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100

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101 node_subst_cost(G1.nodes[n1], G2.nodes[n2]),

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102 node_del_cost(G1.nodes[n1]),

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103 node_ins_cost(G2.nodes[n2]).

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104

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105 That is, the functions will receive the node attribute

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106 dictionaries as inputs. The functions are expected to return

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107 positive numeric values.

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108

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109 Function node_subst_cost overrides node_match if specified.

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110 If neither node_match nor node_subst_cost are specified then

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111 default node substitution cost of 0 is used (node attributes

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112 are not considered during matching).

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113

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114 If node_del_cost is not specified then default node deletion

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115 cost of 1 is used. If node_ins_cost is not specified then

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116 default node insertion cost of 1 is used.

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117

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118 edge_subst_cost, edge_del_cost, edge_ins_cost : callable

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119 Functions that return the costs of edge substitution, edge

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120 deletion, and edge insertion, respectively.

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121

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122 The functions will be called like

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123

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124 edge_subst_cost(G1[u1][v1], G2[u2][v2]),

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125 edge_del_cost(G1[u1][v1]),

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126 edge_ins_cost(G2[u2][v2]).

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127

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128 That is, the functions will receive the edge attribute

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129 dictionaries as inputs. The functions are expected to return

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130 positive numeric values.

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131

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132 Function edge_subst_cost overrides edge_match if specified.

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133 If neither edge_match nor edge_subst_cost are specified then

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134 default edge substitution cost of 0 is used (edge attributes

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135 are not considered during matching).

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136

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137 If edge_del_cost is not specified then default edge deletion

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138 cost of 1 is used. If edge_ins_cost is not specified then

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139 default edge insertion cost of 1 is used.

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140

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141 upper_bound : numeric

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142 Maximum edit distance to consider. Return None if no edit

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143 distance under or equal to upper_bound exists.

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144

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145 Examples

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146 --------

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147 >>> G1 = nx.cycle_graph(6)

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148 >>> G2 = nx.wheel_graph(7)

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149 >>> nx.graph_edit_distance(G1, G2)

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150 7.0

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151

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152 See Also

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153 --------

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154 optimal_edit_paths, optimize_graph_edit_distance,

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155

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156 is_isomorphic (test for graph edit distance of 0)

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157

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158 References

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159 ----------

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160 .. [1] Zeina Abu-Aisheh, Romain Raveaux, Jean-Yves Ramel, Patrick

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161 Martineau. An Exact Graph Edit Distance Algorithm for Solving

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162 Pattern Recognition Problems. 4th International Conference on

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163 Pattern Recognition Applications and Methods 2015, Jan 2015,

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164 Lisbon, Portugal. 2015,

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165 <10.5220/0005209202710278>. <hal-01168816>

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166 https://hal.archives-ouvertes.fr/hal-01168816

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167

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168 """

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169 bestcost = None

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170 for vertex_path, edge_path, cost in \

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171 optimize_edit_paths(G1, G2, node_match, edge_match,

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172 node_subst_cost, node_del_cost, node_ins_cost,

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173 edge_subst_cost, edge_del_cost, edge_ins_cost,

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174 upper_bound, True):

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175 #assert bestcost is None or cost < bestcost

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176 bestcost = cost

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177 return bestcost

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178

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179

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180 def optimal_edit_paths(G1, G2, node_match=None, edge_match=None,

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181 node_subst_cost=None, node_del_cost=None,

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182 node_ins_cost=None,

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183 edge_subst_cost=None, edge_del_cost=None,

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184 edge_ins_cost=None,

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185 upper_bound=None):

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186 """Returns all minimum-cost edit paths transforming G1 to G2.

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187

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188 Graph edit path is a sequence of node and edge edit operations

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189 transforming graph G1 to graph isomorphic to G2. Edit operations

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190 include substitutions, deletions, and insertions.

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191

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192 Parameters

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193 ----------

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194 G1, G2: graphs

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195 The two graphs G1 and G2 must be of the same type.

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196

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197 node_match : callable

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198 A function that returns True if node n1 in G1 and n2 in G2

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199 should be considered equal during matching.

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200

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201 The function will be called like

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202

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203 node_match(G1.nodes[n1], G2.nodes[n2]).

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204

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205 That is, the function will receive the node attribute

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206 dictionaries for n1 and n2 as inputs.

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207

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208 Ignored if node_subst_cost is specified. If neither

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209 node_match nor node_subst_cost are specified then node

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210 attributes are not considered.

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211

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212 edge_match : callable

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213 A function that returns True if the edge attribute dictionaries

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214 for the pair of nodes (u1, v1) in G1 and (u2, v2) in G2 should

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215 be considered equal during matching.

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216

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217 The function will be called like

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218

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219 edge_match(G1[u1][v1], G2[u2][v2]).

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220

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221 That is, the function will receive the edge attribute

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222 dictionaries of the edges under consideration.

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223

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224 Ignored if edge_subst_cost is specified. If neither

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225 edge_match nor edge_subst_cost are specified then edge

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226 attributes are not considered.

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227

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228 node_subst_cost, node_del_cost, node_ins_cost : callable

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229 Functions that return the costs of node substitution, node

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230 deletion, and node insertion, respectively.

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231

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232 The functions will be called like

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233

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234 node_subst_cost(G1.nodes[n1], G2.nodes[n2]),

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235 node_del_cost(G1.nodes[n1]),

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236 node_ins_cost(G2.nodes[n2]).

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237

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238 That is, the functions will receive the node attribute

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239 dictionaries as inputs. The functions are expected to return

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240 positive numeric values.

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241

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242 Function node_subst_cost overrides node_match if specified.

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243 If neither node_match nor node_subst_cost are specified then

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244 default node substitution cost of 0 is used (node attributes

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245 are not considered during matching).

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246

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247 If node_del_cost is not specified then default node deletion

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248 cost of 1 is used. If node_ins_cost is not specified then

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249 default node insertion cost of 1 is used.

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250

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251 edge_subst_cost, edge_del_cost, edge_ins_cost : callable

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252 Functions that return the costs of edge substitution, edge

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253 deletion, and edge insertion, respectively.

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254

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255 The functions will be called like

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256

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257 edge_subst_cost(G1[u1][v1], G2[u2][v2]),

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258 edge_del_cost(G1[u1][v1]),

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259 edge_ins_cost(G2[u2][v2]).

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260

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261 That is, the functions will receive the edge attribute

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262 dictionaries as inputs. The functions are expected to return

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263 positive numeric values.

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264

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265 Function edge_subst_cost overrides edge_match if specified.

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266 If neither edge_match nor edge_subst_cost are specified then

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267 default edge substitution cost of 0 is used (edge attributes

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268 are not considered during matching).

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269

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270 If edge_del_cost is not specified then default edge deletion

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271 cost of 1 is used. If edge_ins_cost is not specified then

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272 default edge insertion cost of 1 is used.

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273

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274 upper_bound : numeric

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275 Maximum edit distance to consider.

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276

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277 Returns

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278 -------

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279 edit_paths : list of tuples (node_edit_path, edge_edit_path)

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280 node_edit_path : list of tuples (u, v)

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281 edge_edit_path : list of tuples ((u1, v1), (u2, v2))

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282

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283 cost : numeric

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284 Optimal edit path cost (graph edit distance).

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285

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286 Examples

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287 --------

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288 >>> G1 = nx.cycle_graph(6)

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289 >>> G2 = nx.wheel_graph(7)

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290 >>> paths, cost = nx.optimal_edit_paths(G1, G2)

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291 >>> len(paths)

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292 84

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293 >>> cost

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294 7.0

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295

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296 See Also

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297 --------

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298 graph_edit_distance, optimize_edit_paths

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299

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300 References

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301 ----------

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302 .. [1] Zeina Abu-Aisheh, Romain Raveaux, Jean-Yves Ramel, Patrick

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303 Martineau. An Exact Graph Edit Distance Algorithm for Solving

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304 Pattern Recognition Problems. 4th International Conference on

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305 Pattern Recognition Applications and Methods 2015, Jan 2015,

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306 Lisbon, Portugal. 2015,

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307 <10.5220/0005209202710278>. <hal-01168816>

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308 https://hal.archives-ouvertes.fr/hal-01168816

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309

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310 """

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311 paths = list()

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312 bestcost = None

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313 for vertex_path, edge_path, cost in \

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314 optimize_edit_paths(G1, G2, node_match, edge_match,

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315 node_subst_cost, node_del_cost, node_ins_cost,

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316 edge_subst_cost, edge_del_cost, edge_ins_cost,

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317 upper_bound, False):

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318 #assert bestcost is None or cost <= bestcost

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319 if bestcost is not None and cost < bestcost:

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320 paths = list()

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321 paths.append((vertex_path, edge_path))

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322 bestcost = cost

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323 return paths, bestcost

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324

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325

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326 def optimize_graph_edit_distance(G1, G2, node_match=None, edge_match=None,

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327 node_subst_cost=None, node_del_cost=None,

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328 node_ins_cost=None,

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329 edge_subst_cost=None, edge_del_cost=None,

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330 edge_ins_cost=None,

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331 upper_bound=None):

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332 """Returns consecutive approximations of GED (graph edit distance)

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333 between graphs G1 and G2.

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334

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335 Graph edit distance is a graph similarity measure analogous to

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336 Levenshtein distance for strings. It is defined as minimum cost

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337 of edit path (sequence of node and edge edit operations)

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338 transforming graph G1 to graph isomorphic to G2.

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339

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340 Parameters

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341 ----------

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342 G1, G2: graphs

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343 The two graphs G1 and G2 must be of the same type.

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344

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345 node_match : callable

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346 A function that returns True if node n1 in G1 and n2 in G2

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347 should be considered equal during matching.

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348

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349 The function will be called like

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350

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351 node_match(G1.nodes[n1], G2.nodes[n2]).

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352

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353 That is, the function will receive the node attribute

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354 dictionaries for n1 and n2 as inputs.

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355

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356 Ignored if node_subst_cost is specified. If neither

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357 node_match nor node_subst_cost are specified then node

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358 attributes are not considered.

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359

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360 edge_match : callable

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361 A function that returns True if the edge attribute dictionaries

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362 for the pair of nodes (u1, v1) in G1 and (u2, v2) in G2 should

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363 be considered equal during matching.

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364

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365 The function will be called like

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366

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367 edge_match(G1[u1][v1], G2[u2][v2]).

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368

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369 That is, the function will receive the edge attribute

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370 dictionaries of the edges under consideration.

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371

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372 Ignored if edge_subst_cost is specified. If neither

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373 edge_match nor edge_subst_cost are specified then edge

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374 attributes are not considered.

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375

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376 node_subst_cost, node_del_cost, node_ins_cost : callable

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377 Functions that return the costs of node substitution, node

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378 deletion, and node insertion, respectively.

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379

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380 The functions will be called like

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381

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382 node_subst_cost(G1.nodes[n1], G2.nodes[n2]),

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383 node_del_cost(G1.nodes[n1]),

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384 node_ins_cost(G2.nodes[n2]).

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385

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386 That is, the functions will receive the node attribute

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387 dictionaries as inputs. The functions are expected to return

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388 positive numeric values.

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389

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390 Function node_subst_cost overrides node_match if specified.

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391 If neither node_match nor node_subst_cost are specified then

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392 default node substitution cost of 0 is used (node attributes

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393 are not considered during matching).

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394

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395 If node_del_cost is not specified then default node deletion

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396 cost of 1 is used. If node_ins_cost is not specified then

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397 default node insertion cost of 1 is used.

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398

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399 edge_subst_cost, edge_del_cost, edge_ins_cost : callable

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400 Functions that return the costs of edge substitution, edge

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401 deletion, and edge insertion, respectively.

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402

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403 The functions will be called like

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404

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405 edge_subst_cost(G1[u1][v1], G2[u2][v2]),

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406 edge_del_cost(G1[u1][v1]),

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407 edge_ins_cost(G2[u2][v2]).

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408

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409 That is, the functions will receive the edge attribute

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410 dictionaries as inputs. The functions are expected to return

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411 positive numeric values.

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412

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413 Function edge_subst_cost overrides edge_match if specified.

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414 If neither edge_match nor edge_subst_cost are specified then

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415 default edge substitution cost of 0 is used (edge attributes

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416 are not considered during matching).

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417

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418 If edge_del_cost is not specified then default edge deletion

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419 cost of 1 is used. If edge_ins_cost is not specified then

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420 default edge insertion cost of 1 is used.

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421

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422 upper_bound : numeric

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423 Maximum edit distance to consider.

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424

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425 Returns

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426 -------

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427 Generator of consecutive approximations of graph edit distance.

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428

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429 Examples

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430 --------

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431 >>> G1 = nx.cycle_graph(6)

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432 >>> G2 = nx.wheel_graph(7)

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433 >>> for v in nx.optimize_graph_edit_distance(G1, G2):

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434 ... minv = v

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435 >>> minv

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436 7.0

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437

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438 See Also

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439 --------

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440 graph_edit_distance, optimize_edit_paths

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441

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442 References

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443 ----------

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444 .. [1] Zeina Abu-Aisheh, Romain Raveaux, Jean-Yves Ramel, Patrick

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445 Martineau. An Exact Graph Edit Distance Algorithm for Solving

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446 Pattern Recognition Problems. 4th International Conference on

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447 Pattern Recognition Applications and Methods 2015, Jan 2015,

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448 Lisbon, Portugal. 2015,

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449 <10.5220/0005209202710278>. <hal-01168816>

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450 https://hal.archives-ouvertes.fr/hal-01168816

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451 """

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452 for vertex_path, edge_path, cost in \

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453 optimize_edit_paths(G1, G2, node_match, edge_match,

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454 node_subst_cost, node_del_cost, node_ins_cost,

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455 edge_subst_cost, edge_del_cost, edge_ins_cost,

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456 upper_bound, True):

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457 yield cost

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458

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459

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460 def optimize_edit_paths(G1, G2, node_match=None, edge_match=None,

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461 node_subst_cost=None, node_del_cost=None,

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462 node_ins_cost=None,

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463 edge_subst_cost=None, edge_del_cost=None,

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464 edge_ins_cost=None,

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465 upper_bound=None, strictly_decreasing=True):

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466 """GED (graph edit distance) calculation: advanced interface.

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467

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468 Graph edit path is a sequence of node and edge edit operations

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469 transforming graph G1 to graph isomorphic to G2. Edit operations

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470 include substitutions, deletions, and insertions.

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471

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472 Graph edit distance is defined as minimum cost of edit path.

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473

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474 Parameters

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475 ----------

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476 G1, G2: graphs

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477 The two graphs G1 and G2 must be of the same type.

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478

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479 node_match : callable

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480 A function that returns True if node n1 in G1 and n2 in G2

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481 should be considered equal during matching.

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482

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483 The function will be called like

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484

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485 node_match(G1.nodes[n1], G2.nodes[n2]).

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486

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487 That is, the function will receive the node attribute

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488 dictionaries for n1 and n2 as inputs.

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489

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490 Ignored if node_subst_cost is specified. If neither

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491 node_match nor node_subst_cost are specified then node

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492 attributes are not considered.

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493

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494 edge_match : callable

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495 A function that returns True if the edge attribute dictionaries

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496 for the pair of nodes (u1, v1) in G1 and (u2, v2) in G2 should

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497 be considered equal during matching.

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498

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499 The function will be called like

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500

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501 edge_match(G1[u1][v1], G2[u2][v2]).

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502

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503 That is, the function will receive the edge attribute

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504 dictionaries of the edges under consideration.

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505

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506 Ignored if edge_subst_cost is specified. If neither

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507 edge_match nor edge_subst_cost are specified then edge

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508 attributes are not considered.

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509

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510 node_subst_cost, node_del_cost, node_ins_cost : callable

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511 Functions that return the costs of node substitution, node

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512 deletion, and node insertion, respectively.

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513

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514 The functions will be called like

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515

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516 node_subst_cost(G1.nodes[n1], G2.nodes[n2]),

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517 node_del_cost(G1.nodes[n1]),

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518 node_ins_cost(G2.nodes[n2]).

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519

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520 That is, the functions will receive the node attribute

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521 dictionaries as inputs. The functions are expected to return

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522 positive numeric values.

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523

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524 Function node_subst_cost overrides node_match if specified.

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525 If neither node_match nor node_subst_cost are specified then

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526 default node substitution cost of 0 is used (node attributes

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527 are not considered during matching).

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528

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529 If node_del_cost is not specified then default node deletion

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530 cost of 1 is used. If node_ins_cost is not specified then

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531 default node insertion cost of 1 is used.

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532

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533 edge_subst_cost, edge_del_cost, edge_ins_cost : callable

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534 Functions that return the costs of edge substitution, edge

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535 deletion, and edge insertion, respectively.

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536

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537 The functions will be called like

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538

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539 edge_subst_cost(G1[u1][v1], G2[u2][v2]),

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540 edge_del_cost(G1[u1][v1]),

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541 edge_ins_cost(G2[u2][v2]).

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542

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543 That is, the functions will receive the edge attribute

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544 dictionaries as inputs. The functions are expected to return

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545 positive numeric values.

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546

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547 Function edge_subst_cost overrides edge_match if specified.

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548 If neither edge_match nor edge_subst_cost are specified then

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549 default edge substitution cost of 0 is used (edge attributes

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550 are not considered during matching).

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551

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552 If edge_del_cost is not specified then default edge deletion

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553 cost of 1 is used. If edge_ins_cost is not specified then

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554 default edge insertion cost of 1 is used.

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555

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556 upper_bound : numeric

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557 Maximum edit distance to consider.

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558

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559 strictly_decreasing : bool

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560 If True, return consecutive approximations of strictly

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561 decreasing cost. Otherwise, return all edit paths of cost

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562 less than or equal to the previous minimum cost.

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563

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564 Returns

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565 -------

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566 Generator of tuples (node_edit_path, edge_edit_path, cost)

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567 node_edit_path : list of tuples (u, v)

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568 edge_edit_path : list of tuples ((u1, v1), (u2, v2))

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569 cost : numeric

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570

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571 See Also

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572 --------

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573 graph_edit_distance, optimize_graph_edit_distance, optimal_edit_paths

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574

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575 References

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576 ----------

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577 .. [1] Zeina Abu-Aisheh, Romain Raveaux, Jean-Yves Ramel, Patrick

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578 Martineau. An Exact Graph Edit Distance Algorithm for Solving

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579 Pattern Recognition Problems. 4th International Conference on

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580 Pattern Recognition Applications and Methods 2015, Jan 2015,

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581 Lisbon, Portugal. 2015,

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582 <10.5220/0005209202710278>. <hal-01168816>

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583 https://hal.archives-ouvertes.fr/hal-01168816

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584

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585 """

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586 # TODO: support DiGraph

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587

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588 import numpy as np

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589 from scipy.optimize import linear_sum_assignment

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590

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591 class CostMatrix:

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592 def __init__(self, C, lsa_row_ind, lsa_col_ind, ls):

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593 #assert C.shape[0] == len(lsa_row_ind)

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594 #assert C.shape[1] == len(lsa_col_ind)

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595 #assert len(lsa_row_ind) == len(lsa_col_ind)

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596 #assert set(lsa_row_ind) == set(range(len(lsa_row_ind)))

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597 #assert set(lsa_col_ind) == set(range(len(lsa_col_ind)))

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598 #assert ls == C[lsa_row_ind, lsa_col_ind].sum()

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599 self.C = C

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600 self.lsa_row_ind = lsa_row_ind

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601 self.lsa_col_ind = lsa_col_ind

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602 self.ls = ls

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603

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604 def make_CostMatrix(C, m, n):

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605 #assert(C.shape == (m + n, m + n))

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606 lsa_row_ind, lsa_col_ind = linear_sum_assignment(C)

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607

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608 # Fixup dummy assignments:

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609 # each substitution i<->j should have dummy assignment m+j<->n+i

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610 # NOTE: fast reduce of Cv relies on it

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611 #assert len(lsa_row_ind) == len(lsa_col_ind)

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612 indexes = zip(range(len(lsa_row_ind)), lsa_row_ind, lsa_col_ind)

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613 subst_ind = list(k for k, i, j in indexes if i < m and j < n)

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614 indexes = zip(range(len(lsa_row_ind)), lsa_row_ind, lsa_col_ind)

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615 dummy_ind = list(k for k, i, j in indexes if i >= m and j >= n)

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616 #assert len(subst_ind) == len(dummy_ind)

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617 lsa_row_ind[dummy_ind] = lsa_col_ind[subst_ind] + m

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618 lsa_col_ind[dummy_ind] = lsa_row_ind[subst_ind] + n

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619

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620 return CostMatrix(C, lsa_row_ind, lsa_col_ind,

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621 C[lsa_row_ind, lsa_col_ind].sum())

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622

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623 def extract_C(C, i, j, m, n):

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624 #assert(C.shape == (m + n, m + n))

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625 row_ind = [k in i or k - m in j for k in range(m + n)]

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626 col_ind = [k in j or k - n in i for k in range(m + n)]

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627 return C[row_ind, :][:, col_ind]

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628

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629 def reduce_C(C, i, j, m, n):

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630 #assert(C.shape == (m + n, m + n))

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631 row_ind = [k not in i and k - m not in j for k in range(m + n)]

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632 col_ind = [k not in j and k - n not in i for k in range(m + n)]

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633 return C[row_ind, :][:, col_ind]

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634

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635 def reduce_ind(ind, i):

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636 #assert set(ind) == set(range(len(ind)))

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637 rind = ind[[k not in i for k in ind]]

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638 for k in set(i):

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639 rind[rind >= k] -= 1

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640 return rind

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641

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642 def match_edges(u, v, pending_g, pending_h, Ce, matched_uv=[]):

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643 """

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644 Parameters:

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645 u, v: matched vertices, u=None or v=None for

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646 deletion/insertion

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647 pending_g, pending_h: lists of edges not yet mapped

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648 Ce: CostMatrix of pending edge mappings

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649 matched_uv: partial vertex edit path

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650 list of tuples (u, v) of previously matched vertex

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651 mappings u<->v, u=None or v=None for

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652 deletion/insertion

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653

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654 Returns:

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655 list of (i, j): indices of edge mappings g<->h

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656 localCe: local CostMatrix of edge mappings

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657 (basically submatrix of Ce at cross of rows i, cols j)

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658 """

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659 M = len(pending_g)

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660 N = len(pending_h)

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661 #assert Ce.C.shape == (M + N, M + N)

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662

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663 g_ind = [i for i in range(M) if pending_g[i][:2] == (u, u) or

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664 any(pending_g[i][:2] in ((p, u), (u, p))

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665 for p, q in matched_uv)]

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666 h_ind = [j for j in range(N) if pending_h[j][:2] == (v, v) or

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667 any(pending_h[j][:2] in ((q, v), (v, q))

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668 for p, q in matched_uv)]

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669 m = len(g_ind)

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670 n = len(h_ind)

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671

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672 if m or n:

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673 C = extract_C(Ce.C, g_ind, h_ind, M, N)

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674 #assert C.shape == (m + n, m + n)

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675

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676 # Forbid structurally invalid matches

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677 # NOTE: inf remembered from Ce construction

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678 for k, i in zip(range(m), g_ind):

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679 g = pending_g[i][:2]

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680 for l, j in zip(range(n), h_ind):

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681 h = pending_h[j][:2]

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682 if nx.is_directed(G1) or nx.is_directed(G2):

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683 if any(g == (p, u) and h == (q, v) or

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684 g == (u, p) and h == (v, q)

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685 for p, q in matched_uv):

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686 continue

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687 else:

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688 if any(g in ((p, u), (u, p)) and h in ((q, v), (v, q))

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689 for p, q in matched_uv):

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690 continue

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691 if g == (u, u):

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692 continue

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693 if h == (v, v):

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694 continue

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695 C[k, l] = inf

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696

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697 localCe = make_CostMatrix(C, m, n)

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698 ij = list((g_ind[k] if k < m else M + h_ind[l],

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699 h_ind[l] if l < n else N + g_ind[k])

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700 for k, l in zip(localCe.lsa_row_ind, localCe.lsa_col_ind)

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701 if k < m or l < n)

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702

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diff changeset

703 else:

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diff changeset

704 ij = []

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diff changeset

705 localCe = CostMatrix(np.empty((0, 0)), [], [], 0)

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parents:

diff changeset

706

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diff changeset

707 return ij, localCe

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parents:

diff changeset

708

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diff changeset

709 def reduce_Ce(Ce, ij, m, n):

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parents:

diff changeset

710 if len(ij):

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parents:

diff changeset

711 i, j = zip(*ij)

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parents:

diff changeset

712 m_i = m - sum(1 for t in i if t < m)

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parents:

diff changeset

713 n_j = n - sum(1 for t in j if t < n)

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diff changeset

714 return make_CostMatrix(reduce_C(Ce.C, i, j, m, n), m_i, n_j)

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diff changeset

715 else:

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diff changeset

716 return Ce

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parents:

diff changeset

717

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diff changeset

718 def get_edit_ops(matched_uv, pending_u, pending_v, Cv,

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parents:

diff changeset

719 pending_g, pending_h, Ce, matched_cost):

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diff changeset

720 """

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diff changeset

721 Parameters:

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diff changeset

722 matched_uv: partial vertex edit path

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diff changeset

723 list of tuples (u, v) of vertex mappings u<->v,

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diff changeset

724 u=None or v=None for deletion/insertion

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diff changeset

725 pending_u, pending_v: lists of vertices not yet mapped

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diff changeset

726 Cv: CostMatrix of pending vertex mappings

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diff changeset

727 pending_g, pending_h: lists of edges not yet mapped

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diff changeset

728 Ce: CostMatrix of pending edge mappings

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diff changeset

729 matched_cost: cost of partial edit path

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parents:

diff changeset

730

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diff changeset

731 Returns:

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diff changeset

732 sequence of

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diff changeset

733 (i, j): indices of vertex mapping u<->v

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diff changeset

734 Cv_ij: reduced CostMatrix of pending vertex mappings

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parents:

diff changeset

735 (basically Cv with row i, col j removed)

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parents:

diff changeset

736 list of (x, y): indices of edge mappings g<->h

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parents:

diff changeset

737 Ce_xy: reduced CostMatrix of pending edge mappings

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parents:

diff changeset

738 (basically Ce with rows x, cols y removed)

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parents:

diff changeset

739 cost: total cost of edit operation

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diff changeset

740 NOTE: most promising ops first

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diff changeset

741 """

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parents:

diff changeset

742 m = len(pending_u)

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parents:

diff changeset

743 n = len(pending_v)

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parents:

diff changeset

744 #assert Cv.C.shape == (m + n, m + n)

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diff changeset

745

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diff changeset

746 # 1) a vertex mapping from optimal linear sum assignment

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parents:

diff changeset

747 i, j = min((k, l) for k, l in zip(Cv.lsa_row_ind, Cv.lsa_col_ind)

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guerler

parents:

diff changeset

748 if k < m or l < n)

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parents:

diff changeset

749 xy, localCe = match_edges(pending_u[i] if i < m else None,

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guerler

parents:

diff changeset

750 pending_v[j] if j < n else None,

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guerler

parents:

diff changeset

751 pending_g, pending_h, Ce, matched_uv)

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parents:

diff changeset

752 Ce_xy = reduce_Ce(Ce, xy, len(pending_g), len(pending_h))

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guerler

parents:

diff changeset

753 #assert Ce.ls <= localCe.ls + Ce_xy.ls

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guerler

parents:

diff changeset

754 if prune(matched_cost + Cv.ls + localCe.ls + Ce_xy.ls):

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parents:

diff changeset

755 pass

56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"

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parents:

diff changeset

756 else:

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parents:

diff changeset

757 # get reduced Cv efficiently

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parents:

diff changeset

758 Cv_ij = CostMatrix(reduce_C(Cv.C, (i,), (j,), m, n),

56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"

guerler

parents:

diff changeset

759 reduce_ind(Cv.lsa_row_ind, (i, m + j)),

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guerler

parents:

diff changeset

760 reduce_ind(Cv.lsa_col_ind, (j, n + i)),

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guerler

parents:

diff changeset

761 Cv.ls - Cv.C[i, j])

56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"

guerler

parents:

diff changeset

762 yield (i, j), Cv_ij, xy, Ce_xy, Cv.C[i, j] + localCe.ls

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guerler

parents:

diff changeset

763

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parents:

diff changeset

764 # 2) other candidates, sorted by lower-bound cost estimate

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parents:

diff changeset

765 other = list()

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diff changeset

766 fixed_i, fixed_j = i, j

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parents:

diff changeset

767 if m <= n:

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parents:

diff changeset

768 candidates = ((t, fixed_j) for t in range(m + n)

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guerler

parents:

diff changeset

769 if t != fixed_i and (t < m or t == m + fixed_j))

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parents:

diff changeset

770 else:

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parents:

diff changeset

771 candidates = ((fixed_i, t) for t in range(m + n)

56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"

guerler

parents:

diff changeset

772 if t != fixed_j and (t < n or t == n + fixed_i))

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parents:

diff changeset

773 for i, j in candidates:

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guerler

parents:

diff changeset

774 if prune(matched_cost + Cv.C[i, j] + Ce.ls):

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parents:

diff changeset

775 continue

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parents:

diff changeset

776 Cv_ij = make_CostMatrix(reduce_C(Cv.C, (i,), (j,), m, n),

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guerler

parents:

diff changeset

777 m - 1 if i < m else m,

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guerler

parents:

diff changeset

778 n - 1 if j < n else n)

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parents:

diff changeset

779 #assert Cv.ls <= Cv.C[i, j] + Cv_ij.ls

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guerler

parents:

diff changeset

780 if prune(matched_cost + Cv.C[i, j] + Cv_ij.ls + Ce.ls):

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guerler

parents:

diff changeset

781 continue

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diff changeset

782 xy, localCe = match_edges(pending_u[i] if i < m else None,

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guerler

parents:

diff changeset

783 pending_v[j] if j < n else None,

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parents:

diff changeset

784 pending_g, pending_h, Ce, matched_uv)

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guerler

parents:

diff changeset

785 if prune(matched_cost + Cv.C[i, j] + Cv_ij.ls + localCe.ls):

56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"

guerler

parents:

diff changeset

786 continue

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parents:

diff changeset

787 Ce_xy = reduce_Ce(Ce, xy, len(pending_g), len(pending_h))

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guerler

parents:

diff changeset

788 #assert Ce.ls <= localCe.ls + Ce_xy.ls

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guerler

parents:

diff changeset

789 if prune(matched_cost + Cv.C[i, j] + Cv_ij.ls + localCe.ls +

56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"

guerler

parents:

diff changeset

790 Ce_xy.ls):

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guerler

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diff changeset

791 continue

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guerler

parents:

diff changeset

792 other.append(((i, j), Cv_ij, xy, Ce_xy, Cv.C[i, j] + localCe.ls))

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guerler

parents:

diff changeset

793

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parents:

diff changeset

794 # yield from

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guerler

parents:

diff changeset

795 for t in sorted(other, key=lambda t: t[4] + t[1].ls + t[3].ls):

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parents:

diff changeset

796 yield t

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guerler

parents:

diff changeset

797

56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"

guerler

parents:

diff changeset

798 def get_edit_paths(matched_uv, pending_u, pending_v, Cv,

56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"

guerler

parents:

diff changeset

799 matched_gh, pending_g, pending_h, Ce, matched_cost):

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guerler

parents:

diff changeset

800 """

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guerler

parents:

diff changeset

801 Parameters:

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guerler

parents:

diff changeset

802 matched_uv: partial vertex edit path

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guerler

parents:

diff changeset

803 list of tuples (u, v) of vertex mappings u<->v,

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guerler

parents:

diff changeset

804 u=None or v=None for deletion/insertion

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guerler

parents:

diff changeset

805 pending_u, pending_v: lists of vertices not yet mapped

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guerler

parents:

diff changeset

806 Cv: CostMatrix of pending vertex mappings

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parents:

diff changeset

807 matched_gh: partial edge edit path

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parents:

diff changeset

808 list of tuples (g, h) of edge mappings g<->h,

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guerler

parents:

diff changeset

809 g=None or h=None for deletion/insertion

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guerler

parents:

diff changeset

810 pending_g, pending_h: lists of edges not yet mapped

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guerler

parents:

diff changeset

811 Ce: CostMatrix of pending edge mappings

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parents:

diff changeset

812 matched_cost: cost of partial edit path

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guerler

parents:

diff changeset

813

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guerler

parents:

diff changeset

814 Returns:

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guerler

parents:

diff changeset

815 sequence of (vertex_path, edge_path, cost)

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guerler

parents:

diff changeset

816 vertex_path: complete vertex edit path

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guerler

parents:

diff changeset

817 list of tuples (u, v) of vertex mappings u<->v,

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guerler

parents:

diff changeset

818 u=None or v=None for deletion/insertion

56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"

guerler

parents:

diff changeset

819 edge_path: complete edge edit path

56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"

guerler

parents:

diff changeset

820 list of tuples (g, h) of edge mappings g<->h,

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guerler

parents:

diff changeset

821 g=None or h=None for deletion/insertion

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guerler

parents:

diff changeset

822 cost: total cost of edit path

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guerler

parents:

diff changeset

823 NOTE: path costs are non-increasing

56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"

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parents:

diff changeset

824 """

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825 #debug_print('matched-uv:', matched_uv)

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diff changeset

826 #debug_print('matched-gh:', matched_gh)

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827 #debug_print('matched-cost:', matched_cost)

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828 #debug_print('pending-u:', pending_u)

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829 #debug_print('pending-v:', pending_v)

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830 #debug_print(Cv.C)

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831 #assert list(sorted(G1.nodes)) == list(sorted(list(u for u, v in matched_uv if u is not None) + pending_u))

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832 #assert list(sorted(G2.nodes)) == list(sorted(list(v for u, v in matched_uv if v is not None) + pending_v))

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833 #debug_print('pending-g:', pending_g)

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diff changeset

834 #debug_print('pending-h:', pending_h)

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835 #debug_print(Ce.C)

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836 #assert list(sorted(G1.edges)) == list(sorted(list(g for g, h in matched_gh if g is not None) + pending_g))

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837 #assert list(sorted(G2.edges)) == list(sorted(list(h for g, h in matched_gh if h is not None) + pending_h))

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838 #debug_print()

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839

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840 if prune(matched_cost + Cv.ls + Ce.ls):

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diff changeset

841 return

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842

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843 if not max(len(pending_u), len(pending_v)):

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844 #assert not len(pending_g)

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845 #assert not len(pending_h)

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846 # path completed!

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847 #assert matched_cost <= maxcost.value

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848 maxcost.value = min(maxcost.value, matched_cost)

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849 yield matched_uv, matched_gh, matched_cost

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850

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851 else:

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852 edit_ops = get_edit_ops(matched_uv, pending_u, pending_v, Cv,

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853 pending_g, pending_h, Ce, matched_cost)

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854 for ij, Cv_ij, xy, Ce_xy, edit_cost in edit_ops:

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diff changeset

855 i, j = ij

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856 #assert Cv.C[i, j] + sum(Ce.C[t] for t in xy) == edit_cost

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diff changeset

857 if prune(matched_cost + edit_cost + Cv_ij.ls + Ce_xy.ls):

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diff changeset

858 continue

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859

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diff changeset

860 # dive deeper

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861 u = pending_u.pop(i) if i < len(pending_u) else None

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862 v = pending_v.pop(j) if j < len(pending_v) else None

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863 matched_uv.append((u, v))

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864 for x, y in xy:

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diff changeset

865 len_g = len(pending_g)

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diff changeset

866 len_h = len(pending_h)

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diff changeset

867 matched_gh.append((pending_g[x] if x < len_g else None,

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868 pending_h[y] if y < len_h else None))

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diff changeset

869 sortedx = list(sorted(x for x, y in xy))

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870 sortedy = list(sorted(y for x, y in xy))

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871 G = list((pending_g.pop(x) if x < len(pending_g) else None)

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872 for x in reversed(sortedx))

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873 H = list((pending_h.pop(y) if y < len(pending_h) else None)

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874 for y in reversed(sortedy))

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875

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876 # yield from

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877 for t in get_edit_paths(matched_uv, pending_u, pending_v,

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diff changeset

878 Cv_ij,

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879 matched_gh, pending_g, pending_h,

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diff changeset

880 Ce_xy,

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881 matched_cost + edit_cost):

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882 yield t

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883

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884 # backtrack

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885 if u is not None:

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diff changeset

886 pending_u.insert(i, u)

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887 if v is not None:

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888 pending_v.insert(j, v)

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889 matched_uv.pop()

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890 for x, g in zip(sortedx, reversed(G)):

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891 if g is not None:

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892 pending_g.insert(x, g)

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893 for y, h in zip(sortedy, reversed(H)):

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894 if h is not None:

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diff changeset

895 pending_h.insert(y, h)

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diff changeset

896 for t in xy:

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diff changeset

897 matched_gh.pop()

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diff changeset

898

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899 # Initialization

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diff changeset

900

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901 pending_u = list(G1.nodes)

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902 pending_v = list(G2.nodes)

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903

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diff changeset

904 # cost matrix of vertex mappings

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905 m = len(pending_u)

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906 n = len(pending_v)

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907 C = np.zeros((m + n, m + n))

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908 if node_subst_cost:

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909 C[0:m, 0:n] = np.array([node_subst_cost(G1.nodes[u], G2.nodes[v])

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diff changeset

910 for u in pending_u for v in pending_v]

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diff changeset

911 ).reshape(m, n)

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diff changeset

912 elif node_match:

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diff changeset

913 C[0:m, 0:n] = np.array([1 - int(node_match(G1.nodes[u], G2.nodes[v]))

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diff changeset

914 for u in pending_u for v in pending_v]

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diff changeset

915 ).reshape(m, n)

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916 else:

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917 # all zeroes

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918 pass

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919 #assert not min(m, n) or C[0:m, 0:n].min() >= 0

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920 if node_del_cost:

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diff changeset

921 del_costs = [node_del_cost(G1.nodes[u]) for u in pending_u]

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diff changeset

922 else:

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diff changeset

923 del_costs = [1] * len(pending_u)

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924 #assert not m or min(del_costs) >= 0

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925 if node_ins_cost:

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diff changeset

926 ins_costs = [node_ins_cost(G2.nodes[v]) for v in pending_v]

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diff changeset

927 else:

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928 ins_costs = [1] * len(pending_v)

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diff changeset

929 #assert not n or min(ins_costs) >= 0

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diff changeset

930 inf = C[0:m, 0:n].sum() + sum(del_costs) + sum(ins_costs) + 1

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diff changeset

931 C[0:m, n:n + m] = np.array([del_costs[i] if i == j else inf

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parents:

diff changeset

932 for i in range(m) for j in range(m)]

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parents:

diff changeset

933 ).reshape(m, m)

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parents:

diff changeset

934 C[m:m + n, 0:n] = np.array([ins_costs[i] if i == j else inf

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parents:

diff changeset

935 for i in range(n) for j in range(n)]

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parents:

diff changeset

936 ).reshape(n, n)

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diff changeset

937 Cv = make_CostMatrix(C, m, n)

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parents:

diff changeset

938 #debug_print('Cv: {} x {}'.format(m, n))

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diff changeset

939 #debug_print(Cv.C)

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diff changeset

940

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diff changeset

941 pending_g = list(G1.edges)

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diff changeset

942 pending_h = list(G2.edges)

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diff changeset

943

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diff changeset

944 # cost matrix of edge mappings

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945 m = len(pending_g)

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946 n = len(pending_h)

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947 C = np.zeros((m + n, m + n))

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948 if edge_subst_cost:

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949 C[0:m, 0:n] = np.array([edge_subst_cost(G1.edges[g], G2.edges[h])

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950 for g in pending_g for h in pending_h]

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951 ).reshape(m, n)

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952 elif edge_match:

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953 C[0:m, 0:n] = np.array([1 - int(edge_match(G1.edges[g], G2.edges[h]))

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954 for g in pending_g for h in pending_h]

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955 ).reshape(m, n)

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956 else:

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957 # all zeroes

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958 pass

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959 #assert not min(m, n) or C[0:m, 0:n].min() >= 0

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960 if edge_del_cost:

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961 del_costs = [edge_del_cost(G1.edges[g]) for g in pending_g]

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962 else:

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963 del_costs = [1] * len(pending_g)

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964 #assert not m or min(del_costs) >= 0

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965 if edge_ins_cost:

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966 ins_costs = [edge_ins_cost(G2.edges[h]) for h in pending_h]

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967 else:

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968 ins_costs = [1] * len(pending_h)

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969 #assert not n or min(ins_costs) >= 0

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970 inf = C[0:m, 0:n].sum() + sum(del_costs) + sum(ins_costs) + 1

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971 C[0:m, n:n + m] = np.array([del_costs[i] if i == j else inf

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972 for i in range(m) for j in range(m)]

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973 ).reshape(m, m)

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974 C[m:m + n, 0:n] = np.array([ins_costs[i] if i == j else inf

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975 for i in range(n) for j in range(n)]

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976 ).reshape(n, n)

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977 Ce = make_CostMatrix(C, m, n)

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978 #debug_print('Ce: {} x {}'.format(m, n))

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979 #debug_print(Ce.C)

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980 #debug_print()

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981

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982 class MaxCost:

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983 def __init__(self):

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984 # initial upper-bound estimate

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985 # NOTE: should work for empty graph

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986 self.value = Cv.C.sum() + Ce.C.sum() + 1

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987 maxcost = MaxCost()

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988

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989 def prune(cost):

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990 if upper_bound is not None:

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991 if cost > upper_bound:

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992 return True

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993 if cost > maxcost.value:

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994 return True

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995 elif strictly_decreasing and cost >= maxcost.value:

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996 return True

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997

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998 # Now go!

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999

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1000 for vertex_path, edge_path, cost in \

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1001 get_edit_paths([], pending_u, pending_v, Cv,

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1002 [], pending_g, pending_h, Ce, 0):

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1003 #assert sorted(G1.nodes) == sorted(u for u, v in vertex_path if u is not None)

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1004 #assert sorted(G2.nodes) == sorted(v for u, v in vertex_path if v is not None)

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1005 #assert sorted(G1.edges) == sorted(g for g, h in edge_path if g is not None)

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1006 #assert sorted(G2.edges) == sorted(h for g, h in edge_path if h is not None)

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1007 #print(vertex_path, edge_path, cost, file = sys.stderr)

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1008 #assert cost == maxcost.value

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1009 yield list(vertex_path), list(edge_path), cost

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1010

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1011

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1012 def _is_close(d1, d2, atolerance=0, rtolerance=0):

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1013 """Determines whether two adjacency matrices are within

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1014 a provided tolerance.

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1015

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1016 Parameters

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1017 ----------

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1018 d1 : dict

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1019 Adjacency dictionary

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1020

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1021 d2 : dict

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1022 Adjacency dictionary

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1023

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1024 atolerance : float

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1025 Some scalar tolerance value to determine closeness

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1026

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1027 rtolerance : float

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1028 A scalar tolerance value that will be some proportion

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1029 of ``d2``'s value

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1030

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1031 Returns

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1032 -------

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1033 closeness : bool

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1034 If all of the nodes within ``d1`` and ``d2`` are within

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1035 a predefined tolerance, they are considered "close" and

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1036 this method will return True. Otherwise, this method will

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1037 return False.

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1038

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1039 """

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1040 # Pre-condition: d1 and d2 have the same keys at each level if they

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1041 # are dictionaries.

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1042 if not isinstance(d1, dict) and not isinstance(d2, dict):

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1043 return abs(d1 - d2) <= atolerance + rtolerance * abs(d2)

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1044 return all(all(_is_close(d1[u][v], d2[u][v]) for v in d1[u]) for u in d1)

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1045

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1046

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1047 def simrank_similarity(G, source=None, target=None, importance_factor=0.9,

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1048 max_iterations=100, tolerance=1e-4):

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1049 """Returns the SimRank similarity of nodes in the graph ``G``.

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1050

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1051 SimRank is a similarity metric that says "two objects are considered

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1052 to be similar if they are referenced by similar objects." [1]_.

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1053

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1054 The pseudo-code definition from the paper is::

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1055

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1056 def simrank(G, u, v):

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1057 in_neighbors_u = G.predecessors(u)

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1058 in_neighbors_v = G.predecessors(v)

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1059 scale = C / (len(in_neighbors_u) * len(in_neighbors_v))

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1060 return scale * sum(simrank(G, w, x)

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1061 for w, x in product(in_neighbors_u,

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1062 in_neighbors_v))

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1063

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1064 where ``G`` is the graph, ``u`` is the source, ``v`` is the target,

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1065 and ``C`` is a float decay or importance factor between 0 and 1.

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1066

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1067 The SimRank algorithm for determining node similarity is defined in

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1068 [2]_.

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1069

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1070 Parameters

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1071 ----------

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1072 G : NetworkX graph

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1073 A NetworkX graph

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1074

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1075 source : node

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1076 If this is specified, the returned dictionary maps each node

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1077 ``v`` in the graph to the similarity between ``source`` and

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1078 ``v``.

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1079

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1080 target : node

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1081 If both ``source`` and ``target`` are specified, the similarity

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1082 value between ``source`` and ``target`` is returned. If

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1083 ``target`` is specified but ``source`` is not, this argument is

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1084 ignored.

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1085

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1086 importance_factor : float

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1087 The relative importance of indirect neighbors with respect to

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1088 direct neighbors.

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1089

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1090 max_iterations : integer

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1091 Maximum number of iterations.

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1092

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1093 tolerance : float

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1094 Error tolerance used to check convergence. When an iteration of

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1095 the algorithm finds that no similarity value changes more than

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1096 this amount, the algorithm halts.

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1097

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1098 Returns

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1099 -------

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1100 similarity : dictionary or float

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1101 If ``source`` and ``target`` are both ``None``, this returns a

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1102 dictionary of dictionaries, where keys are node pairs and value

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1103 are similarity of the pair of nodes.

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1104

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1105 If ``source`` is not ``None`` but ``target`` is, this returns a

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1106 dictionary mapping node to the similarity of ``source`` and that

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1107 node.

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1108

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1109 If neither ``source`` nor ``target`` is ``None``, this returns

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1110 the similarity value for the given pair of nodes.

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1111

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1112 Examples

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1113 --------

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1114 If the nodes of the graph are numbered from zero to *n - 1*, where *n*

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1115 is the number of nodes in the graph, you can create a SimRank matrix

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1116 from the return value of this function where the node numbers are

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1117 the row and column indices of the matrix::

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1118

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1119 >>> import networkx as nx

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1120 >>> from numpy import array

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1121 >>> G = nx.cycle_graph(4)

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1122 >>> sim = nx.simrank_similarity(G)

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1123 >>> lol = [[sim[u][v] for v in sorted(sim[u])] for u in sorted(sim)]

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1124 >>> sim_array = array(lol)

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1125

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1126 References

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1127 ----------

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1128 .. [1] https://en.wikipedia.org/wiki/SimRank

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1129 .. [2] G. Jeh and J. Widom.

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1130 "SimRank: a measure of structural-context similarity",

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1131 In KDD'02: Proceedings of the Eighth ACM SIGKDD

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1132 International Conference on Knowledge Discovery and Data Mining,

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1133 pp. 538--543. ACM Press, 2002.

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1134 """

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1135 prevsim = None

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1136

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1137 # build up our similarity adjacency dictionary output

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1138 newsim = {u: {v: 1 if u == v else 0 for v in G} for u in G}

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1139

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1140 # These functions compute the update to the similarity value of the nodes

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1141 # `u` and `v` with respect to the previous similarity values.

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1142 avg_sim = lambda s: sum(newsim[w][x] for (w, x) in s) / len(s) if s else 0.0

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1143 sim = lambda u, v: importance_factor * avg_sim(list(product(G[u], G[v])))

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1144

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1145 for _ in range(max_iterations):

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1146 if prevsim and _is_close(prevsim, newsim, tolerance):

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1147 break

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1148 prevsim = newsim

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1149 newsim = {u: {v: sim(u, v) if u is not v else 1

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1150 for v in newsim[u]} for u in newsim}

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1151

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1152 if source is not None and target is not None:

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1153 return newsim[source][target]

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1154 if source is not None:

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1155 return newsim[source]

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1156 return newsim

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1157

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1158

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1159 def simrank_similarity_numpy(G, source=None, target=None, importance_factor=0.9,

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1160 max_iterations=100, tolerance=1e-4):

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1161 """Calculate SimRank of nodes in ``G`` using matrices with ``numpy``.

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1162

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1163 The SimRank algorithm for determining node similarity is defined in

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1164 [1]_.

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1165

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1166 Parameters

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1167 ----------

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1168 G : NetworkX graph

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1169 A NetworkX graph

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1170

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1171 source : node

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1172 If this is specified, the returned dictionary maps each node

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1173 ``v`` in the graph to the similarity between ``source`` and

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1174 ``v``.

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1175

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1176 target : node

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1177 If both ``source`` and ``target`` are specified, the similarity

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1178 value between ``source`` and ``target`` is returned. If

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1179 ``target`` is specified but ``source`` is not, this argument is

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1180 ignored.

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1181

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1182 importance_factor : float

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1183 The relative importance of indirect neighbors with respect to

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1184 direct neighbors.

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1185

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1186 max_iterations : integer

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1187 Maximum number of iterations.

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1188

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1189 tolerance : float

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1190 Error tolerance used to check convergence. When an iteration of

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1191 the algorithm finds that no similarity value changes more than

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1192 this amount, the algorithm halts.

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1193

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1194 Returns

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1195 -------

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1196 similarity : dictionary or float

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1197 If ``source`` and ``target`` are both ``None``, this returns a

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1198 dictionary of dictionaries, where keys are node pairs and value

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1199 are similarity of the pair of nodes.

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1200

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1201 If ``source`` is not ``None`` but ``target`` is, this returns a

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1202 dictionary mapping node to the similarity of ``source`` and that

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1203 node.

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1204

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1205 If neither ``source`` nor ``target`` is ``None``, this returns

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1206 the similarity value for the given pair of nodes.

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1207

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1208 Examples

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1209 --------

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1210 >>> import networkx as nx

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1211 >>> from numpy import array

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1212 >>> G = nx.cycle_graph(4)

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1213 >>> sim = nx.simrank_similarity_numpy(G)

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1214

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1215 References

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1216 ----------

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1217 .. [1] G. Jeh and J. Widom.

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1218 "SimRank: a measure of structural-context similarity",

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1219 In KDD'02: Proceedings of the Eighth ACM SIGKDD

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1220 International Conference on Knowledge Discovery and Data Mining,

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1221 pp. 538--543. ACM Press, 2002.

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1222 """

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1223 # This algorithm follows roughly

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1224 #

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1225 # S = max{C * (A.T * S * A), I}

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1226 #

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1227 # where C is the importance factor, A is the column normalized

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1228 # adjacency matrix, and I is the identity matrix.

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1229 import numpy as np

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1230 adjacency_matrix = nx.to_numpy_array(G)

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1231

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1232 # column-normalize the ``adjacency_matrix``

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1233 adjacency_matrix /= adjacency_matrix.sum(axis=0)

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1234

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1235 newsim = np.eye(adjacency_matrix.shape[0], dtype=np.float64)

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1236 for _ in range(max_iterations):

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1237 prevsim = np.copy(newsim)

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1238 newsim = importance_factor * np.matmul(

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1239 np.matmul(adjacency_matrix.T, prevsim), adjacency_matrix)

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1240 np.fill_diagonal(newsim, 1.0)

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1241

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1242 if np.allclose(prevsim, newsim, atol=tolerance):

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1243 break

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1244

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1245 if source is not None and target is not None:

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1246 return newsim[source, target]

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1247 if source is not None:

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1248 return newsim[source]

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1249 return newsim

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1250

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1251

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1252 # fixture for pytest

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1253 def setup_module(module):

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1254 import pytest

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1255 numpy = pytest.importorskip('numpy')

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1256 scipy = pytest.importorskip('scipy')

Mercurial > repos > guerler > springsuite

annotate planemo/lib/python3.7/site-packages/networkx/algorithms/similarity.py @ 1:56ad4e20f292 draft