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