Mercurial > repos > guerler > springsuite

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

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
"planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
author guerler
date Fri, 31 Jul 2020 00:32:28 -0400
parents
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
1
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
1 # tournament.py - functions for tournament graphs
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
2 #
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
3 # Copyright 2015 NetworkX developers.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
4 #
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
5 # This file is part of NetworkX.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
6 #
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
7 # NetworkX is distributed under a BSD license; see LICENSE.txt for more
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
8 # information.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
9 """Functions concerning tournament graphs.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
10
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
11 A `tournament graph`_ is a complete oriented graph. In other words, it
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
12 is a directed graph in which there is exactly one directed edge joining
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
13 each pair of distinct nodes. For each function in this module that
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
14 accepts a graph as input, you must provide a tournament graph. The
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
15 responsibility is on the caller to ensure that the graph is a tournament
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
16 graph.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
17
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
18 To access the functions in this module, you must access them through the
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
19 :mod:`networkx.algorithms.tournament` module::
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
20
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
21 >>> import networkx as nx
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
22 >>> from networkx.algorithms import tournament
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
23 >>> G = nx.DiGraph([(0, 1), (1, 2), (2, 0)])
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
24 >>> tournament.is_tournament(G)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
25 True
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
26
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
27 .. _tournament graph: https://en.wikipedia.org/wiki/Tournament_%28graph_theory%29
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
28
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
29 """
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
30 from itertools import combinations
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
31
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
32 import networkx as nx
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
33 from networkx.algorithms.simple_paths import is_simple_path as is_path
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
34 from networkx.utils import arbitrary_element
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
35 from networkx.utils import not_implemented_for
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
36 from networkx.utils import py_random_state
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
37
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
38 __all__ = ['hamiltonian_path', 'is_reachable', 'is_strongly_connected',
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
39 'is_tournament', 'random_tournament', 'score_sequence']
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 index_satisfying(iterable, condition):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
43 """Returns the index of the first element in `iterable` that
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
44 satisfies the given condition.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
45
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
46 If no such element is found (that is, when the iterable is
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
47 exhausted), this returns the length of the iterable (that is, one
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
48 greater than the last index of the iterable).
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
49
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
50 `iterable` must not be empty. If `iterable` is empty, this
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
51 function raises :exc:`ValueError`.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
52
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
53 """
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
54 # Pre-condition: iterable must not be empty.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
55 for i, x in enumerate(iterable):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
56 if condition(x):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
57 return i
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
58 # If we reach the end of the iterable without finding an element
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
59 # that satisfies the condition, return the length of the iterable,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
60 # which is one greater than the index of its last element. If the
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
61 # iterable was empty, `i` will not be defined, so we raise an
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
62 # exception.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
63 try:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
64 return i + 1
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
65 except NameError:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
66 raise ValueError('iterable must be non-empty')
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
67
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
68
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
69 @not_implemented_for('undirected')
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
70 @not_implemented_for('multigraph')
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
71 def is_tournament(G):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
72 """Returns True if and only if `G` is a tournament.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
73
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
74 A tournament is a directed graph, with neither self-loops nor
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
75 multi-edges, in which there is exactly one directed edge joining
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
76 each pair of distinct nodes.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
77
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
78 Parameters
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
79 ----------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
80 G : NetworkX graph
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
81 A directed graph representing a tournament.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
82
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
83 Returns
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
84 -------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
85 bool
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
86 Whether the given graph is a tournament graph.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
87
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
88 Notes
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
89 -----
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
90 Some definitions require a self-loop on each node, but that is not
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
91 the convention used here.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
92
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
93 """
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
94 # In a tournament, there is exactly one directed edge joining each pair.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
95 return (all((v in G[u]) ^ (u in G[v]) for u, v in combinations(G, 2)) and
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
96 nx.number_of_selfloops(G) == 0)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
97
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
98
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
99 @not_implemented_for('undirected')
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
100 @not_implemented_for('multigraph')
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
101 def hamiltonian_path(G):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
102 """Returns a Hamiltonian path in the given tournament graph.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
103
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
104 Each tournament has a Hamiltonian path. If furthermore, the
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
105 tournament is strongly connected, then the returned Hamiltonian path
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
106 is a Hamiltonian cycle (by joining the endpoints of the path).
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
107
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
108 Parameters
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
109 ----------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
110 G : NetworkX graph
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
111 A directed graph representing a tournament.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
112
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
113 Returns
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
114 -------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
115 bool
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
116 Whether the given graph is a tournament graph.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
117
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
118 Notes
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
119 -----
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
120 This is a recursive implementation with an asymptotic running time
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
121 of $O(n^2)$, ignoring multiplicative polylogarithmic factors, where
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
122 $n$ is the number of nodes in the graph.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
123
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
124 """
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
125 if len(G) == 0:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
126 return []
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
127 if len(G) == 1:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
128 return [arbitrary_element(G)]
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
129 v = arbitrary_element(G)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
130 hampath = hamiltonian_path(G.subgraph(set(G) - {v}))
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
131 # Get the index of the first node in the path that does *not* have
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
132 # an edge to `v`, then insert `v` before that node.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
133 index = index_satisfying(hampath, lambda u: v not in G[u])
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
134 hampath.insert(index, v)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
135 return hampath
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
136
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
137
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
138 @py_random_state(1)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
139 def random_tournament(n, seed=None):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
140 r"""Returns a random tournament graph on `n` nodes.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
141
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
142 Parameters
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
143 ----------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
144 n : int
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
145 The number of nodes in the returned graph.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
146 seed : integer, random_state, or None (default)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
147 Indicator of random number generation state.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
148 See :ref:`Randomness<randomness>`.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
149
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
150 Returns
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
151 -------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
152 bool
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
153 Whether the given graph is a tournament graph.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
154
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
155 Notes
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
156 -----
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
157 This algorithm adds, for each pair of distinct nodes, an edge with
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
158 uniformly random orientation. In other words, `\binom{n}{2}` flips
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
159 of an unbiased coin decide the orientations of the edges in the
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
160 graph.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
161
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
162 """
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
163 # Flip an unbiased coin for each pair of distinct nodes.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
164 coins = (seed.random() for i in range((n * (n - 1)) // 2))
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
165 pairs = combinations(range(n), 2)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
166 edges = ((u, v) if r < 0.5 else (v, u) for (u, v), r in zip(pairs, coins))
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
167 return nx.DiGraph(edges)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
168
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
169
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
170 @not_implemented_for('undirected')
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
171 @not_implemented_for('multigraph')
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
172 def score_sequence(G):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
173 """Returns the score sequence for the given tournament graph.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
174
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
175 The score sequence is the sorted list of the out-degrees of the
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
176 nodes of the graph.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
177
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
178 Parameters
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
179 ----------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
180 G : NetworkX graph
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
181 A directed graph representing a tournament.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
182
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
183 Returns
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
184 -------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
185 list
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
186 A sorted list of the out-degrees of the nodes of `G`.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
187
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
188 """
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
189 return sorted(d for v, d in G.out_degree())
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
190
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
191
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
192 @not_implemented_for('undirected')
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
193 @not_implemented_for('multigraph')
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
194 def tournament_matrix(G):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
195 r"""Returns the tournament matrix for the given tournament graph.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
196
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
197 This function requires SciPy.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
198
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
199 The *tournament matrix* of a tournament graph with edge set *E* is
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
200 the matrix *T* defined by
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
201
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
202 .. math::
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
203
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
204 T_{i j} =
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
205 \begin{cases}
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
206 +1 & \text{if } (i, j) \in E \\
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
207 -1 & \text{if } (j, i) \in E \\
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
208 0 & \text{if } i == j.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
209 \end{cases}
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
210
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
211 An equivalent definition is `T = A - A^T`, where *A* is the
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
212 adjacency matrix of the graph `G`.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
213
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
214 Parameters
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
215 ----------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
216 G : NetworkX graph
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
217 A directed graph representing a tournament.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
218
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
219 Returns
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
220 -------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
221 SciPy sparse matrix
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
222 The tournament matrix of the tournament graph `G`.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
223
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
224 Raises
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
225 ------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
226 ImportError
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
227 If SciPy is not available.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
228
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
229 """
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
230 A = nx.adjacency_matrix(G)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
231 return A - A.T
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
232
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
233
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
234 @not_implemented_for('undirected')
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
235 @not_implemented_for('multigraph')
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
236 def is_reachable(G, s, t):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
237 """Decides whether there is a path from `s` to `t` in the
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
238 tournament.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
239
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
240 This function is more theoretically efficient than the reachability
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
241 checks than the shortest path algorithms in
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
242 :mod:`networkx.algorithms.shortest_paths`.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
243
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
244 The given graph **must** be a tournament, otherwise this function's
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
245 behavior is undefined.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
246
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
247 Parameters
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
248 ----------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
249 G : NetworkX graph
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
250 A directed graph representing a tournament.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
251
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
252 s : node
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
253 A node in the graph.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
254
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
255 t : node
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
256 A node in the graph.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
257
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
258 Returns
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
259 -------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
260 bool
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
261 Whether there is a path from `s` to `t` in `G`.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
262
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
263 Notes
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
264 -----
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
265 Although this function is more theoretically efficient than the
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
266 generic shortest path functions, a speedup requires the use of
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
267 parallelism. Though it may in the future, the current implementation
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
268 does not use parallelism, thus you may not see much of a speedup.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
269
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
270 This algorithm comes from [1].
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
271
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
272 References
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
273 ----------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
274 .. [1] Tantau, Till.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
275 "A note on the complexity of the reachability problem for
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
276 tournaments."
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
277 *Electronic Colloquium on Computational Complexity*. 2001.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
278 <http://eccc.hpi-web.de/report/2001/092/>
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
279
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
280 """
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
281
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
282 def two_neighborhood(G, v):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
283 """Returns the set of nodes at distance at most two from `v`.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
284
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
285 `G` must be a graph and `v` a node in that graph.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
286
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
287 The returned set includes the nodes at distance zero (that is,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
288 the node `v` itself), the nodes at distance one (that is, the
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
289 out-neighbors of `v`), and the nodes at distance two.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
290
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
291 """
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
292 # TODO This is trivially parallelizable.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
293 return {x for x in G
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
294 if x == v or x in G[v] or
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
295 any(is_path(G, [v, z, x]) for z in G)}
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
296
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
297 def is_closed(G, nodes):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
298 """Decides whether the given set of nodes is closed.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
299
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
300 A set *S* of nodes is *closed* if for each node *u* in the graph
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
301 not in *S* and for each node *v* in *S*, there is an edge from
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
302 *u* to *v*.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
303
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
304 """
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
305 # TODO This is trivially parallelizable.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
306 return all(v in G[u] for u in set(G) - nodes for v in nodes)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
307
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
308 # TODO This is trivially parallelizable.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
309 neighborhoods = [two_neighborhood(G, v) for v in G]
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
310 return all(not (is_closed(G, S) and s in S and t not in S)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
311 for S in neighborhoods)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
312
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
313
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
314 @not_implemented_for('undirected')
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
315 @not_implemented_for('multigraph')
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
316 def is_strongly_connected(G):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
317 """Decides whether the given tournament is strongly connected.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
318
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
319 This function is more theoretically efficient than the
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
320 :func:`~networkx.algorithms.components.is_strongly_connected`
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
321 function.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
322
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
323 The given graph **must** be a tournament, otherwise this function's
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
324 behavior is undefined.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
325
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
326 Parameters
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
327 ----------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
328 G : NetworkX graph
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
329 A directed graph representing a tournament.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
330
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
331 Returns
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
332 -------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
333 bool
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
334 Whether the tournament is strongly connected.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
335
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
336 Notes
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
337 -----
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
338 Although this function is more theoretically efficient than the
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
339 generic strong connectivity function, a speedup requires the use of
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
340 parallelism. Though it may in the future, the current implementation
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
341 does not use parallelism, thus you may not see much of a speedup.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
342
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
343 This algorithm comes from [1].
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
344
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
345 References
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
346 ----------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
347 .. [1] Tantau, Till.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
348 "A note on the complexity of the reachability problem for
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
349 tournaments."
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
350 *Electronic Colloquium on Computational Complexity*. 2001.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
351 <http://eccc.hpi-web.de/report/2001/092/>
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
352
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
353 """
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
354 # TODO This is trivially parallelizable.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
355 return all(is_reachable(G, u, v) for u in G for v in G)