Mercurial > repos > guerler > springsuite

comparison planemo/lib/python3.7/site-packages/networkx/algorithms/triads.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
comparison
equal deleted inserted replaced
0:d30785e31577 1:56ad4e20f292
1 # triads.py - functions for analyzing triads of a graph
2 #
3 # Copyright 2015 NetworkX developers.
4 # Copyright 2011 Reya Group <http://www.reyagroup.com>
5 # Copyright 2011 Alex Levenson <alex@isnotinvain.com>
6 # Copyright 2011 Diederik van Liere <diederik.vanliere@rotman.utoronto.ca>
7 #
8 # This file is part of NetworkX.
9 #
10 # NetworkX is distributed under a BSD license; see LICENSE.txt for more
11 # information.
12 """Functions for analyzing triads of a graph."""
13
14 from networkx.utils import not_implemented_for
15
16 __author__ = '\n'.join(['Alex Levenson (alex@isnontinvain.com)',
17 'Diederik van Liere (diederik.vanliere@rotman.utoronto.ca)'])
18
19 __all__ = ['triadic_census']
20
21 #: The integer codes representing each type of triad.
22 #:
23 #: Triads that are the same up to symmetry have the same code.
24 TRICODES = (1, 2, 2, 3, 2, 4, 6, 8, 2, 6, 5, 7, 3, 8, 7, 11, 2, 6, 4, 8, 5, 9,
25 9, 13, 6, 10, 9, 14, 7, 14, 12, 15, 2, 5, 6, 7, 6, 9, 10, 14, 4, 9,
26 9, 12, 8, 13, 14, 15, 3, 7, 8, 11, 7, 12, 14, 15, 8, 14, 13, 15,
27 11, 15, 15, 16)
28
29 #: The names of each type of triad. The order of the elements is
30 #: important: it corresponds to the tricodes given in :data:`TRICODES`.
31 TRIAD_NAMES = ('003', '012', '102', '021D', '021U', '021C', '111D', '111U',
32 '030T', '030C', '201', '120D', '120U', '120C', '210', '300')
33
34
35 #: A dictionary mapping triad code to triad name.
36 TRICODE_TO_NAME = {i: TRIAD_NAMES[code - 1] for i, code in enumerate(TRICODES)}
37
38
39 def _tricode(G, v, u, w):
40 """Returns the integer code of the given triad.
41
42 This is some fancy magic that comes from Batagelj and Mrvar's paper. It
43 treats each edge joining a pair of `v`, `u`, and `w` as a bit in
44 the binary representation of an integer.
45
46 """
47 combos = ((v, u, 1), (u, v, 2), (v, w, 4), (w, v, 8), (u, w, 16),
48 (w, u, 32))
49 return sum(x for u, v, x in combos if v in G[u])
50
51
52 @not_implemented_for('undirected')
53 def triadic_census(G):
54 """Determines the triadic census of a directed graph.
55
56 The triadic census is a count of how many of the 16 possible types of
57 triads are present in a directed graph.
58
59 Parameters
60 ----------
61 G : digraph
62 A NetworkX DiGraph
63
64 Returns
65 -------
66 census : dict
67 Dictionary with triad names as keys and number of occurrences as values.
68
69 Notes
70 -----
71 This algorithm has complexity $O(m)$ where $m$ is the number of edges in
72 the graph.
73
74 See also
75 --------
76 triad_graph
77
78 References
79 ----------
80 .. [1] Vladimir Batagelj and Andrej Mrvar, A subquadratic triad census
81 algorithm for large sparse networks with small maximum degree,
82 University of Ljubljana,
83 http://vlado.fmf.uni-lj.si/pub/networks/doc/triads/triads.pdf
84
85 """
86 # Initialize the count for each triad to be zero.
87 census = {name: 0 for name in TRIAD_NAMES}
88 n = len(G)
89 # m = dict(zip(G, range(n)))
90 m = {v: i for i, v in enumerate(G)}
91 for v in G:
92 vnbrs = set(G.pred[v]) | set(G.succ[v])
93 for u in vnbrs:
94 if m[u] <= m[v]:
95 continue
96 neighbors = (vnbrs | set(G.succ[u]) | set(G.pred[u])) - {u, v}
97 # Calculate dyadic triads instead of counting them.
98 if v in G[u] and u in G[v]:
99 census['102'] += n - len(neighbors) - 2
100 else:
101 census['012'] += n - len(neighbors) - 2
102 # Count connected triads.
103 for w in neighbors:
104 if m[u] < m[w] or (m[v] < m[w] < m[u] and
105 v not in G.pred[w] and
106 v not in G.succ[w]):
107 code = _tricode(G, v, u, w)
108 census[TRICODE_TO_NAME[code]] += 1
109
110 # null triads = total number of possible triads - all found triads
111 #
112 # Use integer division here, since we know this formula guarantees an
113 # integral value.
114 census['003'] = ((n * (n - 1) * (n - 2)) // 6) - sum(census.values())
115 return census