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

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"planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
author guerler
date Fri, 31 Jul 2020 00:32:28 -0400
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0:d30785e31577 1:56ad4e20f292
1 # -*- coding: utf-8 -*-
2 # chains.py - functions for finding chains in a graph
3 #
4 # Copyright 2004-2019 NetworkX developers.
5 #
6 # This file is part of NetworkX.
7 #
8 # NetworkX is distributed under a BSD license; see LICENSE.txt for more
9 # information.
10 """Functions for finding chains in a graph."""
11
12 import networkx as nx
13 from networkx.utils import not_implemented_for
14
15
16 @not_implemented_for('directed')
17 @not_implemented_for('multigraph')
18 def chain_decomposition(G, root=None):
19 """Returns the chain decomposition of a graph.
20
21 The *chain decomposition* of a graph with respect a depth-first
22 search tree is a set of cycles or paths derived from the set of
23 fundamental cycles of the tree in the following manner. Consider
24 each fundamental cycle with respect to the given tree, represented
25 as a list of edges beginning with the nontree edge oriented away
26 from the root of the tree. For each fundamental cycle, if it
27 overlaps with any previous fundamental cycle, just take the initial
28 non-overlapping segment, which is a path instead of a cycle. Each
29 cycle or path is called a *chain*. For more information, see [1]_.
30
31 Parameters
32 ----------
33 G : undirected graph
34
35 root : node (optional)
36 A node in the graph `G`. If specified, only the chain
37 decomposition for the connected component containing this node
38 will be returned. This node indicates the root of the depth-first
39 search tree.
40
41 Yields
42 ------
43 chain : list
44 A list of edges representing a chain. There is no guarantee on
45 the orientation of the edges in each chain (for example, if a
46 chain includes the edge joining nodes 1 and 2, the chain may
47 include either (1, 2) or (2, 1)).
48
49 Raises
50 ------
51 NodeNotFound
52 If `root` is not in the graph `G`.
53
54 Notes
55 -----
56 The worst-case running time of this implementation is linear in the
57 number of nodes and number of edges [1]_.
58
59 References
60 ----------
61 .. [1] Jens M. Schmidt (2013). "A simple test on 2-vertex-
62 and 2-edge-connectivity." *Information Processing Letters*,
63 113, 241–244. Elsevier. <https://doi.org/10.1016/j.ipl.2013.01.016>
64
65 """
66
67 def _dfs_cycle_forest(G, root=None):
68 """Builds a directed graph composed of cycles from the given graph.
69
70 `G` is an undirected simple graph. `root` is a node in the graph
71 from which the depth-first search is started.
72
73 This function returns both the depth-first search cycle graph
74 (as a :class:`~networkx.DiGraph`) and the list of nodes in
75 depth-first preorder. The depth-first search cycle graph is a
76 directed graph whose edges are the edges of `G` oriented toward
77 the root if the edge is a tree edge and away from the root if
78 the edge is a non-tree edge. If `root` is not specified, this
79 performs a depth-first search on each connected component of `G`
80 and returns a directed forest instead.
81
82 If `root` is not in the graph, this raises :exc:`KeyError`.
83
84 """
85 # Create a directed graph from the depth-first search tree with
86 # root node `root` in which tree edges are directed toward the
87 # root and nontree edges are directed away from the root. For
88 # each node with an incident nontree edge, this creates a
89 # directed cycle starting with the nontree edge and returning to
90 # that node.
91 #
92 # The `parent` node attribute stores the parent of each node in
93 # the DFS tree. The `nontree` edge attribute indicates whether
94 # the edge is a tree edge or a nontree edge.
95 #
96 # We also store the order of the nodes found in the depth-first
97 # search in the `nodes` list.
98 H = nx.DiGraph()
99 nodes = []
100 for u, v, d in nx.dfs_labeled_edges(G, source=root):
101 if d == 'forward':
102 # `dfs_labeled_edges()` yields (root, root, 'forward')
103 # if it is beginning the search on a new connected
104 # component.
105 if u == v:
106 H.add_node(v, parent=None)
107 nodes.append(v)
108 else:
109 H.add_node(v, parent=u)
110 H.add_edge(v, u, nontree=False)
111 nodes.append(v)
112 # `dfs_labeled_edges` considers nontree edges in both
113 # orientations, so we need to not add the edge if it its
114 # other orientation has been added.
115 elif d == 'nontree' and v not in H[u]:
116 H.add_edge(v, u, nontree=True)
117 else:
118 # Do nothing on 'reverse' edges; we only care about
119 # forward and nontree edges.
120 pass
121 return H, nodes
122
123 def _build_chain(G, u, v, visited):
124 """Generate the chain starting from the given nontree edge.
125
126 `G` is a DFS cycle graph as constructed by
127 :func:`_dfs_cycle_graph`. The edge (`u`, `v`) is a nontree edge
128 that begins a chain. `visited` is a set representing the nodes
129 in `G` that have already been visited.
130
131 This function yields the edges in an initial segment of the
132 fundamental cycle of `G` starting with the nontree edge (`u`,
133 `v`) that includes all the edges up until the first node that
134 appears in `visited`. The tree edges are given by the 'parent'
135 node attribute. The `visited` set is updated to add each node in
136 an edge yielded by this function.
137
138 """
139 while v not in visited:
140 yield u, v
141 visited.add(v)
142 u, v = v, G.nodes[v]['parent']
143 yield u, v
144
145 # Create a directed version of H that has the DFS edges directed
146 # toward the root and the nontree edges directed away from the root
147 # (in each connected component).
148 H, nodes = _dfs_cycle_forest(G, root)
149
150 # Visit the nodes again in DFS order. For each node, and for each
151 # nontree edge leaving that node, compute the fundamental cycle for
152 # that nontree edge starting with that edge. If the fundamental
153 # cycle overlaps with any visited nodes, just take the prefix of the
154 # cycle up to the point of visited nodes.
155 #
156 # We repeat this process for each connected component (implicitly,
157 # since `nodes` already has a list of the nodes grouped by connected
158 # component).
159 visited = set()
160 for u in nodes:
161 visited.add(u)
162 # For each nontree edge going out of node u...
163 edges = ((u, v) for u, v, d in H.out_edges(u, data='nontree') if d)
164 for u, v in edges:
165 # Create the cycle or cycle prefix starting with the
166 # nontree edge.
167 chain = list(_build_chain(H, u, v, visited))
168 yield chain