Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/community/centrality.py @ 0:4f3585e2f14b draft default tip
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author | shellac |
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date | Mon, 22 Mar 2021 18:12:50 +0000 |
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1 """Functions for computing communities based on centrality notions.""" |
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2 |
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3 import networkx as nx |
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4 |
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5 __all__ = ["girvan_newman"] |
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6 |
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7 |
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8 def girvan_newman(G, most_valuable_edge=None): |
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9 """Finds communities in a graph using the Girvan–Newman method. |
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10 |
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11 Parameters |
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12 ---------- |
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13 G : NetworkX graph |
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14 |
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15 most_valuable_edge : function |
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16 Function that takes a graph as input and outputs an edge. The |
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17 edge returned by this function will be recomputed and removed at |
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18 each iteration of the algorithm. |
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19 |
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20 If not specified, the edge with the highest |
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21 :func:`networkx.edge_betweenness_centrality` will be used. |
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22 |
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23 Returns |
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24 ------- |
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25 iterator |
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26 Iterator over tuples of sets of nodes in `G`. Each set of node |
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27 is a community, each tuple is a sequence of communities at a |
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28 particular level of the algorithm. |
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29 |
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30 Examples |
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31 -------- |
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32 To get the first pair of communities:: |
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33 |
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34 >>> G = nx.path_graph(10) |
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35 >>> comp = girvan_newman(G) |
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36 >>> tuple(sorted(c) for c in next(comp)) |
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37 ([0, 1, 2, 3, 4], [5, 6, 7, 8, 9]) |
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38 |
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39 To get only the first *k* tuples of communities, use |
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40 :func:`itertools.islice`:: |
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41 |
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42 >>> import itertools |
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43 >>> G = nx.path_graph(8) |
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44 >>> k = 2 |
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45 >>> comp = girvan_newman(G) |
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46 >>> for communities in itertools.islice(comp, k): |
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47 ... print(tuple(sorted(c) for c in communities)) # doctest: +SKIP |
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48 ... |
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49 ([0, 1, 2, 3], [4, 5, 6, 7]) |
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50 ([0, 1], [2, 3], [4, 5, 6, 7]) |
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51 |
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52 To stop getting tuples of communities once the number of communities |
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53 is greater than *k*, use :func:`itertools.takewhile`:: |
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54 |
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55 >>> import itertools |
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56 >>> G = nx.path_graph(8) |
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57 >>> k = 4 |
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58 >>> comp = girvan_newman(G) |
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59 >>> limited = itertools.takewhile(lambda c: len(c) <= k, comp) |
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60 >>> for communities in limited: |
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61 ... print(tuple(sorted(c) for c in communities)) # doctest: +SKIP |
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62 ... |
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63 ([0, 1, 2, 3], [4, 5, 6, 7]) |
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64 ([0, 1], [2, 3], [4, 5, 6, 7]) |
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65 ([0, 1], [2, 3], [4, 5], [6, 7]) |
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66 |
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67 To just choose an edge to remove based on the weight:: |
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68 |
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69 >>> from operator import itemgetter |
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70 >>> G = nx.path_graph(10) |
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71 >>> edges = G.edges() |
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72 >>> nx.set_edge_attributes(G, {(u, v): v for u, v in edges}, "weight") |
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73 >>> def heaviest(G): |
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74 ... u, v, w = max(G.edges(data="weight"), key=itemgetter(2)) |
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75 ... return (u, v) |
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76 ... |
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77 >>> comp = girvan_newman(G, most_valuable_edge=heaviest) |
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78 >>> tuple(sorted(c) for c in next(comp)) |
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79 ([0, 1, 2, 3, 4, 5, 6, 7, 8], [9]) |
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80 |
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81 To utilize edge weights when choosing an edge with, for example, the |
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82 highest betweenness centrality:: |
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83 |
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84 >>> from networkx import edge_betweenness_centrality as betweenness |
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85 >>> def most_central_edge(G): |
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86 ... centrality = betweenness(G, weight="weight") |
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87 ... return max(centrality, key=centrality.get) |
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88 ... |
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89 >>> G = nx.path_graph(10) |
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90 >>> comp = girvan_newman(G, most_valuable_edge=most_central_edge) |
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91 >>> tuple(sorted(c) for c in next(comp)) |
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92 ([0, 1, 2, 3, 4], [5, 6, 7, 8, 9]) |
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93 |
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94 To specify a different ranking algorithm for edges, use the |
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95 `most_valuable_edge` keyword argument:: |
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96 |
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97 >>> from networkx import edge_betweenness_centrality |
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98 >>> from random import random |
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99 >>> def most_central_edge(G): |
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100 ... centrality = edge_betweenness_centrality(G) |
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101 ... max_cent = max(centrality.values()) |
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102 ... # Scale the centrality values so they are between 0 and 1, |
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103 ... # and add some random noise. |
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104 ... centrality = {e: c / max_cent for e, c in centrality.items()} |
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105 ... # Add some random noise. |
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106 ... centrality = {e: c + random() for e, c in centrality.items()} |
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107 ... return max(centrality, key=centrality.get) |
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108 ... |
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109 >>> G = nx.path_graph(10) |
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110 >>> comp = girvan_newman(G, most_valuable_edge=most_central_edge) |
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111 |
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112 Notes |
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113 ----- |
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114 The Girvan–Newman algorithm detects communities by progressively |
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115 removing edges from the original graph. The algorithm removes the |
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116 "most valuable" edge, traditionally the edge with the highest |
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117 betweenness centrality, at each step. As the graph breaks down into |
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118 pieces, the tightly knit community structure is exposed and the |
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119 result can be depicted as a dendrogram. |
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120 |
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121 """ |
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122 # If the graph is already empty, simply return its connected |
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123 # components. |
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124 if G.number_of_edges() == 0: |
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125 yield tuple(nx.connected_components(G)) |
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126 return |
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127 # If no function is provided for computing the most valuable edge, |
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128 # use the edge betweenness centrality. |
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129 if most_valuable_edge is None: |
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130 |
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131 def most_valuable_edge(G): |
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132 """Returns the edge with the highest betweenness centrality |
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133 in the graph `G`. |
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134 |
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135 """ |
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136 # We have guaranteed that the graph is non-empty, so this |
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137 # dictionary will never be empty. |
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138 betweenness = nx.edge_betweenness_centrality(G) |
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139 return max(betweenness, key=betweenness.get) |
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140 |
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141 # The copy of G here must include the edge weight data. |
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142 g = G.copy().to_undirected() |
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143 # Self-loops must be removed because their removal has no effect on |
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144 # the connected components of the graph. |
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145 g.remove_edges_from(nx.selfloop_edges(g)) |
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146 while g.number_of_edges() > 0: |
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147 yield _without_most_central_edges(g, most_valuable_edge) |
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148 |
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149 |
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150 def _without_most_central_edges(G, most_valuable_edge): |
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151 """Returns the connected components of the graph that results from |
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152 repeatedly removing the most "valuable" edge in the graph. |
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153 |
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154 `G` must be a non-empty graph. This function modifies the graph `G` |
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155 in-place; that is, it removes edges on the graph `G`. |
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156 |
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157 `most_valuable_edge` is a function that takes the graph `G` as input |
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158 (or a subgraph with one or more edges of `G` removed) and returns an |
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159 edge. That edge will be removed and this process will be repeated |
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160 until the number of connected components in the graph increases. |
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161 |
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162 """ |
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163 original_num_components = nx.number_connected_components(G) |
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164 num_new_components = original_num_components |
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165 while num_new_components <= original_num_components: |
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166 edge = most_valuable_edge(G) |
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167 G.remove_edge(*edge) |
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168 new_components = tuple(nx.connected_components(G)) |
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169 num_new_components = len(new_components) |
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170 return new_components |