Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/efficiency_measures.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 """Provides functions for computing the efficiency of nodes and graphs.""" |
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2 |
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3 import networkx as nx |
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4 from networkx.exception import NetworkXNoPath |
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5 from ..utils import not_implemented_for |
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6 |
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7 __all__ = ["efficiency", "local_efficiency", "global_efficiency"] |
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8 |
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9 |
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10 @not_implemented_for("directed") |
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11 def efficiency(G, u, v): |
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12 """Returns the efficiency of a pair of nodes in a graph. |
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13 |
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14 The *efficiency* of a pair of nodes is the multiplicative inverse of the |
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15 shortest path distance between the nodes [1]_. Returns 0 if no path |
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16 between nodes. |
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17 |
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18 Parameters |
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19 ---------- |
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20 G : :class:`networkx.Graph` |
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21 An undirected graph for which to compute the average local efficiency. |
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22 u, v : node |
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23 Nodes in the graph ``G``. |
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24 |
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25 Returns |
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26 ------- |
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27 float |
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28 Multiplicative inverse of the shortest path distance between the nodes. |
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29 |
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30 Notes |
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31 ----- |
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32 Edge weights are ignored when computing the shortest path distances. |
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33 |
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34 See also |
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35 -------- |
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36 local_efficiency |
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37 global_efficiency |
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38 |
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39 References |
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40 ---------- |
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41 .. [1] Latora, Vito, and Massimo Marchiori. |
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42 "Efficient behavior of small-world networks." |
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43 *Physical Review Letters* 87.19 (2001): 198701. |
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44 <https://doi.org/10.1103/PhysRevLett.87.198701> |
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45 |
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46 """ |
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47 try: |
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48 eff = 1 / nx.shortest_path_length(G, u, v) |
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49 except NetworkXNoPath: |
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50 eff = 0 |
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51 return eff |
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52 |
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53 |
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54 @not_implemented_for("directed") |
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55 def global_efficiency(G): |
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56 """Returns the average global efficiency of the graph. |
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57 |
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58 The *efficiency* of a pair of nodes in a graph is the multiplicative |
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59 inverse of the shortest path distance between the nodes. The *average |
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60 global efficiency* of a graph is the average efficiency of all pairs of |
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61 nodes [1]_. |
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62 |
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63 Parameters |
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64 ---------- |
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65 G : :class:`networkx.Graph` |
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66 An undirected graph for which to compute the average global efficiency. |
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67 |
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68 Returns |
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69 ------- |
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70 float |
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71 The average global efficiency of the graph. |
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72 |
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73 Notes |
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74 ----- |
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75 Edge weights are ignored when computing the shortest path distances. |
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76 |
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77 See also |
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78 -------- |
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79 local_efficiency |
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80 |
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81 References |
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82 ---------- |
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83 .. [1] Latora, Vito, and Massimo Marchiori. |
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84 "Efficient behavior of small-world networks." |
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85 *Physical Review Letters* 87.19 (2001): 198701. |
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86 <https://doi.org/10.1103/PhysRevLett.87.198701> |
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87 |
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88 """ |
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89 n = len(G) |
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90 denom = n * (n - 1) |
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91 if denom != 0: |
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92 lengths = nx.all_pairs_shortest_path_length(G) |
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93 g_eff = 0 |
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94 for source, targets in lengths: |
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95 for target, distance in targets.items(): |
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96 if distance > 0: |
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97 g_eff += 1 / distance |
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98 g_eff /= denom |
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99 # g_eff = sum(1 / d for s, tgts in lengths |
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100 # for t, d in tgts.items() if d > 0) / denom |
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101 else: |
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102 g_eff = 0 |
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103 # TODO This can be made more efficient by computing all pairs shortest |
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104 # path lengths in parallel. |
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105 return g_eff |
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106 |
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107 |
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108 @not_implemented_for("directed") |
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109 def local_efficiency(G): |
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110 """Returns the average local efficiency of the graph. |
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111 |
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112 The *efficiency* of a pair of nodes in a graph is the multiplicative |
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113 inverse of the shortest path distance between the nodes. The *local |
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114 efficiency* of a node in the graph is the average global efficiency of the |
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115 subgraph induced by the neighbors of the node. The *average local |
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116 efficiency* is the average of the local efficiencies of each node [1]_. |
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117 |
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118 Parameters |
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119 ---------- |
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120 G : :class:`networkx.Graph` |
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121 An undirected graph for which to compute the average local efficiency. |
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122 |
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123 Returns |
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124 ------- |
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125 float |
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126 The average local efficiency of the graph. |
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127 |
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128 Notes |
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129 ----- |
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130 Edge weights are ignored when computing the shortest path distances. |
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131 |
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132 See also |
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133 -------- |
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134 global_efficiency |
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135 |
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136 References |
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137 ---------- |
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138 .. [1] Latora, Vito, and Massimo Marchiori. |
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139 "Efficient behavior of small-world networks." |
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140 *Physical Review Letters* 87.19 (2001): 198701. |
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141 <https://doi.org/10.1103/PhysRevLett.87.198701> |
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142 |
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143 """ |
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144 # TODO This summation can be trivially parallelized. |
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145 efficiency_list = (global_efficiency(G.subgraph(G[v])) for v in G) |
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146 return sum(efficiency_list) / len(G) |