Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/link_prediction.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 """ |
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2 Link prediction algorithms. |
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3 """ |
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4 |
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5 |
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6 from math import log |
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7 |
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8 import networkx as nx |
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9 from networkx.utils import not_implemented_for |
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10 |
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11 __all__ = [ |
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12 "resource_allocation_index", |
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13 "jaccard_coefficient", |
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14 "adamic_adar_index", |
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15 "preferential_attachment", |
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16 "cn_soundarajan_hopcroft", |
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17 "ra_index_soundarajan_hopcroft", |
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18 "within_inter_cluster", |
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19 "common_neighbor_centrality", |
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20 ] |
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21 |
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22 |
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23 def _apply_prediction(G, func, ebunch=None): |
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24 """Applies the given function to each edge in the specified iterable |
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25 of edges. |
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26 |
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27 `G` is an instance of :class:`networkx.Graph`. |
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28 |
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29 `func` is a function on two inputs, each of which is a node in the |
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30 graph. The function can return anything, but it should return a |
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31 value representing a prediction of the likelihood of a "link" |
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32 joining the two nodes. |
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33 |
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34 `ebunch` is an iterable of pairs of nodes. If not specified, all |
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35 non-edges in the graph `G` will be used. |
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36 |
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37 """ |
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38 if ebunch is None: |
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39 ebunch = nx.non_edges(G) |
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40 return ((u, v, func(u, v)) for u, v in ebunch) |
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41 |
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42 |
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43 @not_implemented_for("directed") |
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44 @not_implemented_for("multigraph") |
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45 def resource_allocation_index(G, ebunch=None): |
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46 r"""Compute the resource allocation index of all node pairs in ebunch. |
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47 |
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48 Resource allocation index of `u` and `v` is defined as |
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49 |
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50 .. math:: |
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51 |
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52 \sum_{w \in \Gamma(u) \cap \Gamma(v)} \frac{1}{|\Gamma(w)|} |
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53 |
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54 where $\Gamma(u)$ denotes the set of neighbors of $u$. |
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55 |
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56 Parameters |
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57 ---------- |
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58 G : graph |
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59 A NetworkX undirected graph. |
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60 |
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61 ebunch : iterable of node pairs, optional (default = None) |
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62 Resource allocation index will be computed for each pair of |
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63 nodes given in the iterable. The pairs must be given as |
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64 2-tuples (u, v) where u and v are nodes in the graph. If ebunch |
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65 is None then all non-existent edges in the graph will be used. |
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66 Default value: None. |
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67 |
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68 Returns |
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69 ------- |
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70 piter : iterator |
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71 An iterator of 3-tuples in the form (u, v, p) where (u, v) is a |
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72 pair of nodes and p is their resource allocation index. |
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73 |
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74 Examples |
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75 -------- |
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76 >>> G = nx.complete_graph(5) |
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77 >>> preds = nx.resource_allocation_index(G, [(0, 1), (2, 3)]) |
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78 >>> for u, v, p in preds: |
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79 ... print(f"({u}, {v}) -> {p:.8f}") |
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80 (0, 1) -> 0.75000000 |
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81 (2, 3) -> 0.75000000 |
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82 |
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83 References |
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84 ---------- |
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85 .. [1] T. Zhou, L. Lu, Y.-C. Zhang. |
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86 Predicting missing links via local information. |
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87 Eur. Phys. J. B 71 (2009) 623. |
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88 https://arxiv.org/pdf/0901.0553.pdf |
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89 """ |
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90 |
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91 def predict(u, v): |
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92 return sum(1 / G.degree(w) for w in nx.common_neighbors(G, u, v)) |
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93 |
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94 return _apply_prediction(G, predict, ebunch) |
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95 |
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96 |
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97 @not_implemented_for("directed") |
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98 @not_implemented_for("multigraph") |
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99 def jaccard_coefficient(G, ebunch=None): |
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100 r"""Compute the Jaccard coefficient of all node pairs in ebunch. |
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101 |
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102 Jaccard coefficient of nodes `u` and `v` is defined as |
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103 |
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104 .. math:: |
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105 |
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106 \frac{|\Gamma(u) \cap \Gamma(v)|}{|\Gamma(u) \cup \Gamma(v)|} |
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107 |
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108 where $\Gamma(u)$ denotes the set of neighbors of $u$. |
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109 |
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110 Parameters |
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111 ---------- |
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112 G : graph |
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113 A NetworkX undirected graph. |
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114 |
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115 ebunch : iterable of node pairs, optional (default = None) |
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116 Jaccard coefficient will be computed for each pair of nodes |
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117 given in the iterable. The pairs must be given as 2-tuples |
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118 (u, v) where u and v are nodes in the graph. If ebunch is None |
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119 then all non-existent edges in the graph will be used. |
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120 Default value: None. |
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121 |
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122 Returns |
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123 ------- |
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124 piter : iterator |
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125 An iterator of 3-tuples in the form (u, v, p) where (u, v) is a |
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126 pair of nodes and p is their Jaccard coefficient. |
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127 |
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128 Examples |
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129 -------- |
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130 >>> G = nx.complete_graph(5) |
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131 >>> preds = nx.jaccard_coefficient(G, [(0, 1), (2, 3)]) |
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132 >>> for u, v, p in preds: |
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133 ... print(f"({u}, {v}) -> {p:.8f}") |
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134 (0, 1) -> 0.60000000 |
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135 (2, 3) -> 0.60000000 |
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136 |
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137 References |
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138 ---------- |
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139 .. [1] D. Liben-Nowell, J. Kleinberg. |
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140 The Link Prediction Problem for Social Networks (2004). |
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141 http://www.cs.cornell.edu/home/kleinber/link-pred.pdf |
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142 """ |
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143 |
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144 def predict(u, v): |
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145 union_size = len(set(G[u]) | set(G[v])) |
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146 if union_size == 0: |
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147 return 0 |
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148 return len(list(nx.common_neighbors(G, u, v))) / union_size |
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149 |
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150 return _apply_prediction(G, predict, ebunch) |
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151 |
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152 |
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153 @not_implemented_for("directed") |
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154 @not_implemented_for("multigraph") |
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155 def adamic_adar_index(G, ebunch=None): |
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156 r"""Compute the Adamic-Adar index of all node pairs in ebunch. |
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157 |
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158 Adamic-Adar index of `u` and `v` is defined as |
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159 |
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160 .. math:: |
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161 |
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162 \sum_{w \in \Gamma(u) \cap \Gamma(v)} \frac{1}{\log |\Gamma(w)|} |
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163 |
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164 where $\Gamma(u)$ denotes the set of neighbors of $u$. |
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165 This index leads to zero-division for nodes only connected via self-loops. |
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166 It is intended to be used when no self-loops are present. |
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167 |
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168 Parameters |
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169 ---------- |
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170 G : graph |
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171 NetworkX undirected graph. |
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172 |
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173 ebunch : iterable of node pairs, optional (default = None) |
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174 Adamic-Adar index will be computed for each pair of nodes given |
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175 in the iterable. The pairs must be given as 2-tuples (u, v) |
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176 where u and v are nodes in the graph. If ebunch is None then all |
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177 non-existent edges in the graph will be used. |
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178 Default value: None. |
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179 |
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180 Returns |
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181 ------- |
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182 piter : iterator |
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183 An iterator of 3-tuples in the form (u, v, p) where (u, v) is a |
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184 pair of nodes and p is their Adamic-Adar index. |
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185 |
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186 Examples |
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187 -------- |
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188 >>> G = nx.complete_graph(5) |
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189 >>> preds = nx.adamic_adar_index(G, [(0, 1), (2, 3)]) |
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190 >>> for u, v, p in preds: |
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191 ... print(f"({u}, {v}) -> {p:.8f}") |
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192 (0, 1) -> 2.16404256 |
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193 (2, 3) -> 2.16404256 |
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194 |
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195 References |
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196 ---------- |
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197 .. [1] D. Liben-Nowell, J. Kleinberg. |
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198 The Link Prediction Problem for Social Networks (2004). |
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199 http://www.cs.cornell.edu/home/kleinber/link-pred.pdf |
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200 """ |
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201 |
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202 def predict(u, v): |
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203 return sum(1 / log(G.degree(w)) for w in nx.common_neighbors(G, u, v)) |
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204 |
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205 return _apply_prediction(G, predict, ebunch) |
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206 |
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207 |
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208 @not_implemented_for("directed") |
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209 @not_implemented_for("multigraph") |
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210 def common_neighbor_centrality(G, ebunch=None, alpha=0.8): |
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211 r"""Return the CCPA score for each pair of nodes. |
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212 |
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213 Compute the Common Neighbor and Centrality based Parameterized Algorithm(CCPA) |
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214 score of all node pairs in ebunch. |
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215 |
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216 CCPA score of `u` and `v` is defined as |
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217 |
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218 .. math:: |
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219 |
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220 \alpha \cdot (|\Gamma (u){\cap }^{}\Gamma (v)|)+(1-\alpha )\cdot \frac{N}{{d}_{uv}} |
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221 |
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222 where $\Gamma(u)$ denotes the set of neighbors of $u$, $\Gamma(v)$ denotes the |
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223 set of neighbors of $v$, $\alpha$ is parameter varies between [0,1], $N$ denotes |
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224 total number of nodes in the Graph and ${d}_{uv}$ denotes shortest distance |
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225 between $u$ and $v$. |
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226 |
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227 This algorithm is based on two vital properties of nodes, namely the number |
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228 of common neighbors and their centrality. Common neighbor refers to the common |
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229 nodes between two nodes. Centrality refers to the prestige that a node enjoys |
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230 in a network. |
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231 |
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232 .. seealso:: |
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233 |
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234 :func:`common_neighbors` |
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235 |
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236 Parameters |
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237 ---------- |
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238 G : graph |
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239 NetworkX undirected graph. |
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240 |
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241 ebunch : iterable of node pairs, optional (default = None) |
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242 Preferential attachment score will be computed for each pair of |
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243 nodes given in the iterable. The pairs must be given as |
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244 2-tuples (u, v) where u and v are nodes in the graph. If ebunch |
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245 is None then all non-existent edges in the graph will be used. |
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246 Default value: None. |
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247 |
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248 alpha : Parameter defined for participation of Common Neighbor |
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249 and Centrality Algorithm share. Default value set to 0.8 |
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250 because author found better performance at 0.8 for all the |
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251 dataset. |
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252 Default value: 0.8 |
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253 |
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254 |
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255 Returns |
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256 ------- |
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257 piter : iterator |
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258 An iterator of 3-tuples in the form (u, v, p) where (u, v) is a |
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259 pair of nodes and p is their Common Neighbor and Centrality based |
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260 Parameterized Algorithm(CCPA) score. |
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261 |
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262 Examples |
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263 -------- |
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264 >>> G = nx.complete_graph(5) |
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265 >>> preds = nx.common_neighbor_centrality(G, [(0, 1), (2, 3)]) |
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266 >>> for u, v, p in preds: |
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267 ... print(f"({u}, {v}) -> {p}") |
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268 (0, 1) -> 3.4000000000000004 |
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269 (2, 3) -> 3.4000000000000004 |
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270 |
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271 References |
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272 ---------- |
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273 .. [1] Ahmad, I., Akhtar, M.U., Noor, S. et al. |
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274 Missing Link Prediction using Common Neighbor and Centrality based Parameterized Algorithm. |
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275 Sci Rep 10, 364 (2020). |
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276 https://doi.org/10.1038/s41598-019-57304-y |
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277 """ |
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278 shortest_path = nx.shortest_path(G) |
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279 |
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280 def predict(u, v): |
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281 return alpha * len(list(nx.common_neighbors(G, u, v))) + (1 - alpha) * ( |
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282 G.number_of_nodes() / (len(shortest_path[u][v]) - 1) |
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283 ) |
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284 |
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285 return _apply_prediction(G, predict, ebunch) |
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286 |
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287 |
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288 @not_implemented_for("directed") |
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289 @not_implemented_for("multigraph") |
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290 def preferential_attachment(G, ebunch=None): |
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291 r"""Compute the preferential attachment score of all node pairs in ebunch. |
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292 |
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293 Preferential attachment score of `u` and `v` is defined as |
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294 |
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295 .. math:: |
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296 |
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297 |\Gamma(u)| |\Gamma(v)| |
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298 |
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299 where $\Gamma(u)$ denotes the set of neighbors of $u$. |
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300 |
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301 Parameters |
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302 ---------- |
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303 G : graph |
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304 NetworkX undirected graph. |
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305 |
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306 ebunch : iterable of node pairs, optional (default = None) |
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307 Preferential attachment score will be computed for each pair of |
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308 nodes given in the iterable. The pairs must be given as |
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309 2-tuples (u, v) where u and v are nodes in the graph. If ebunch |
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310 is None then all non-existent edges in the graph will be used. |
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311 Default value: None. |
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312 |
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313 Returns |
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314 ------- |
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315 piter : iterator |
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316 An iterator of 3-tuples in the form (u, v, p) where (u, v) is a |
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317 pair of nodes and p is their preferential attachment score. |
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318 |
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319 Examples |
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320 -------- |
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321 >>> G = nx.complete_graph(5) |
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322 >>> preds = nx.preferential_attachment(G, [(0, 1), (2, 3)]) |
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323 >>> for u, v, p in preds: |
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324 ... print(f"({u}, {v}) -> {p}") |
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325 (0, 1) -> 16 |
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326 (2, 3) -> 16 |
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327 |
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328 References |
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329 ---------- |
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330 .. [1] D. Liben-Nowell, J. Kleinberg. |
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331 The Link Prediction Problem for Social Networks (2004). |
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332 http://www.cs.cornell.edu/home/kleinber/link-pred.pdf |
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333 """ |
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334 |
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335 def predict(u, v): |
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336 return G.degree(u) * G.degree(v) |
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337 |
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338 return _apply_prediction(G, predict, ebunch) |
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339 |
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340 |
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341 @not_implemented_for("directed") |
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342 @not_implemented_for("multigraph") |
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343 def cn_soundarajan_hopcroft(G, ebunch=None, community="community"): |
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344 r"""Count the number of common neighbors of all node pairs in ebunch |
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345 using community information. |
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346 |
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347 For two nodes $u$ and $v$, this function computes the number of |
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348 common neighbors and bonus one for each common neighbor belonging to |
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349 the same community as $u$ and $v$. Mathematically, |
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350 |
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351 .. math:: |
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352 |
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353 |\Gamma(u) \cap \Gamma(v)| + \sum_{w \in \Gamma(u) \cap \Gamma(v)} f(w) |
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354 |
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355 where $f(w)$ equals 1 if $w$ belongs to the same community as $u$ |
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356 and $v$ or 0 otherwise and $\Gamma(u)$ denotes the set of |
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357 neighbors of $u$. |
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358 |
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359 Parameters |
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360 ---------- |
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361 G : graph |
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362 A NetworkX undirected graph. |
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363 |
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364 ebunch : iterable of node pairs, optional (default = None) |
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365 The score will be computed for each pair of nodes given in the |
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366 iterable. The pairs must be given as 2-tuples (u, v) where u |
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367 and v are nodes in the graph. If ebunch is None then all |
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368 non-existent edges in the graph will be used. |
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369 Default value: None. |
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370 |
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371 community : string, optional (default = 'community') |
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372 Nodes attribute name containing the community information. |
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373 G[u][community] identifies which community u belongs to. Each |
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374 node belongs to at most one community. Default value: 'community'. |
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375 |
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376 Returns |
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377 ------- |
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378 piter : iterator |
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379 An iterator of 3-tuples in the form (u, v, p) where (u, v) is a |
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380 pair of nodes and p is their score. |
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381 |
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382 Examples |
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383 -------- |
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384 >>> G = nx.path_graph(3) |
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385 >>> G.nodes[0]["community"] = 0 |
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386 >>> G.nodes[1]["community"] = 0 |
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387 >>> G.nodes[2]["community"] = 0 |
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388 >>> preds = nx.cn_soundarajan_hopcroft(G, [(0, 2)]) |
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389 >>> for u, v, p in preds: |
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390 ... print(f"({u}, {v}) -> {p}") |
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391 (0, 2) -> 2 |
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392 |
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393 References |
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394 ---------- |
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395 .. [1] Sucheta Soundarajan and John Hopcroft. |
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396 Using community information to improve the precision of link |
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397 prediction methods. |
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398 In Proceedings of the 21st international conference companion on |
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399 World Wide Web (WWW '12 Companion). ACM, New York, NY, USA, 607-608. |
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400 http://doi.acm.org/10.1145/2187980.2188150 |
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401 """ |
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402 |
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403 def predict(u, v): |
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404 Cu = _community(G, u, community) |
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405 Cv = _community(G, v, community) |
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406 cnbors = list(nx.common_neighbors(G, u, v)) |
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407 neighbors = ( |
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408 sum(_community(G, w, community) == Cu for w in cnbors) if Cu == Cv else 0 |
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409 ) |
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410 return len(cnbors) + neighbors |
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411 |
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412 return _apply_prediction(G, predict, ebunch) |
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413 |
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414 |
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415 @not_implemented_for("directed") |
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416 @not_implemented_for("multigraph") |
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417 def ra_index_soundarajan_hopcroft(G, ebunch=None, community="community"): |
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418 r"""Compute the resource allocation index of all node pairs in |
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419 ebunch using community information. |
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420 |
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421 For two nodes $u$ and $v$, this function computes the resource |
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422 allocation index considering only common neighbors belonging to the |
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423 same community as $u$ and $v$. Mathematically, |
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424 |
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425 .. math:: |
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426 |
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427 \sum_{w \in \Gamma(u) \cap \Gamma(v)} \frac{f(w)}{|\Gamma(w)|} |
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428 |
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429 where $f(w)$ equals 1 if $w$ belongs to the same community as $u$ |
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430 and $v$ or 0 otherwise and $\Gamma(u)$ denotes the set of |
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431 neighbors of $u$. |
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432 |
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433 Parameters |
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434 ---------- |
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435 G : graph |
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436 A NetworkX undirected graph. |
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437 |
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438 ebunch : iterable of node pairs, optional (default = None) |
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439 The score will be computed for each pair of nodes given in the |
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440 iterable. The pairs must be given as 2-tuples (u, v) where u |
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441 and v are nodes in the graph. If ebunch is None then all |
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442 non-existent edges in the graph will be used. |
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443 Default value: None. |
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444 |
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445 community : string, optional (default = 'community') |
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446 Nodes attribute name containing the community information. |
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447 G[u][community] identifies which community u belongs to. Each |
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448 node belongs to at most one community. Default value: 'community'. |
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449 |
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450 Returns |
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451 ------- |
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452 piter : iterator |
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453 An iterator of 3-tuples in the form (u, v, p) where (u, v) is a |
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454 pair of nodes and p is their score. |
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455 |
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456 Examples |
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457 -------- |
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458 >>> G = nx.Graph() |
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459 >>> G.add_edges_from([(0, 1), (0, 2), (1, 3), (2, 3)]) |
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460 >>> G.nodes[0]["community"] = 0 |
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461 >>> G.nodes[1]["community"] = 0 |
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462 >>> G.nodes[2]["community"] = 1 |
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463 >>> G.nodes[3]["community"] = 0 |
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464 >>> preds = nx.ra_index_soundarajan_hopcroft(G, [(0, 3)]) |
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465 >>> for u, v, p in preds: |
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466 ... print(f"({u}, {v}) -> {p:.8f}") |
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467 (0, 3) -> 0.50000000 |
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468 |
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469 References |
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470 ---------- |
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471 .. [1] Sucheta Soundarajan and John Hopcroft. |
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472 Using community information to improve the precision of link |
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473 prediction methods. |
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474 In Proceedings of the 21st international conference companion on |
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475 World Wide Web (WWW '12 Companion). ACM, New York, NY, USA, 607-608. |
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476 http://doi.acm.org/10.1145/2187980.2188150 |
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477 """ |
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478 |
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479 def predict(u, v): |
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480 Cu = _community(G, u, community) |
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481 Cv = _community(G, v, community) |
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482 if Cu != Cv: |
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483 return 0 |
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484 cnbors = nx.common_neighbors(G, u, v) |
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485 return sum(1 / G.degree(w) for w in cnbors if _community(G, w, community) == Cu) |
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486 |
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487 return _apply_prediction(G, predict, ebunch) |
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488 |
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489 |
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490 @not_implemented_for("directed") |
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491 @not_implemented_for("multigraph") |
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492 def within_inter_cluster(G, ebunch=None, delta=0.001, community="community"): |
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493 """Compute the ratio of within- and inter-cluster common neighbors |
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494 of all node pairs in ebunch. |
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495 |
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496 For two nodes `u` and `v`, if a common neighbor `w` belongs to the |
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497 same community as them, `w` is considered as within-cluster common |
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498 neighbor of `u` and `v`. Otherwise, it is considered as |
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499 inter-cluster common neighbor of `u` and `v`. The ratio between the |
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500 size of the set of within- and inter-cluster common neighbors is |
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501 defined as the WIC measure. [1]_ |
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502 |
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503 Parameters |
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504 ---------- |
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505 G : graph |
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506 A NetworkX undirected graph. |
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507 |
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508 ebunch : iterable of node pairs, optional (default = None) |
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509 The WIC measure will be computed for each pair of nodes given in |
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510 the iterable. The pairs must be given as 2-tuples (u, v) where |
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511 u and v are nodes in the graph. If ebunch is None then all |
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512 non-existent edges in the graph will be used. |
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513 Default value: None. |
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514 |
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515 delta : float, optional (default = 0.001) |
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516 Value to prevent division by zero in case there is no |
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517 inter-cluster common neighbor between two nodes. See [1]_ for |
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518 details. Default value: 0.001. |
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519 |
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520 community : string, optional (default = 'community') |
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521 Nodes attribute name containing the community information. |
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522 G[u][community] identifies which community u belongs to. Each |
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523 node belongs to at most one community. Default value: 'community'. |
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524 |
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525 Returns |
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526 ------- |
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527 piter : iterator |
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528 An iterator of 3-tuples in the form (u, v, p) where (u, v) is a |
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529 pair of nodes and p is their WIC measure. |
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530 |
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531 Examples |
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532 -------- |
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533 >>> G = nx.Graph() |
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534 >>> G.add_edges_from([(0, 1), (0, 2), (0, 3), (1, 4), (2, 4), (3, 4)]) |
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535 >>> G.nodes[0]["community"] = 0 |
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536 >>> G.nodes[1]["community"] = 1 |
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537 >>> G.nodes[2]["community"] = 0 |
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538 >>> G.nodes[3]["community"] = 0 |
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539 >>> G.nodes[4]["community"] = 0 |
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540 >>> preds = nx.within_inter_cluster(G, [(0, 4)]) |
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541 >>> for u, v, p in preds: |
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542 ... print(f"({u}, {v}) -> {p:.8f}") |
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543 (0, 4) -> 1.99800200 |
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544 >>> preds = nx.within_inter_cluster(G, [(0, 4)], delta=0.5) |
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545 >>> for u, v, p in preds: |
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546 ... print(f"({u}, {v}) -> {p:.8f}") |
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547 (0, 4) -> 1.33333333 |
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548 |
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549 References |
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550 ---------- |
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551 .. [1] Jorge Carlos Valverde-Rebaza and Alneu de Andrade Lopes. |
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552 Link prediction in complex networks based on cluster information. |
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553 In Proceedings of the 21st Brazilian conference on Advances in |
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554 Artificial Intelligence (SBIA'12) |
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555 https://doi.org/10.1007/978-3-642-34459-6_10 |
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556 """ |
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557 if delta <= 0: |
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558 raise nx.NetworkXAlgorithmError("Delta must be greater than zero") |
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559 |
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560 def predict(u, v): |
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561 Cu = _community(G, u, community) |
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562 Cv = _community(G, v, community) |
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563 if Cu != Cv: |
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564 return 0 |
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565 cnbors = set(nx.common_neighbors(G, u, v)) |
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566 within = {w for w in cnbors if _community(G, w, community) == Cu} |
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567 inter = cnbors - within |
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568 return len(within) / (len(inter) + delta) |
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569 |
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570 return _apply_prediction(G, predict, ebunch) |
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571 |
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572 |
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573 def _community(G, u, community): |
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574 """Get the community of the given node.""" |
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575 node_u = G.nodes[u] |
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576 try: |
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577 return node_u[community] |
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578 except KeyError as e: |
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579 raise nx.NetworkXAlgorithmError("No community information") from e |