Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/graph_hashing.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 Functions for hashing graphs to strings. |
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3 Isomorphic graphs should be assigned identical hashes. |
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4 For now, only Weisfeiler-Lehman hashing is implemented. |
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5 """ |
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6 |
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7 from collections import Counter |
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8 from hashlib import blake2b |
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9 |
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10 __all__ = ["weisfeiler_lehman_graph_hash"] |
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11 |
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12 |
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13 def weisfeiler_lehman_graph_hash( |
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14 G, edge_attr=None, node_attr=None, iterations=3, digest_size=16 |
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15 ): |
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16 """Return Weisfeiler Lehman (WL) graph hash. |
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17 |
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18 The function iteratively aggregates and hashes neighbourhoods of each node. |
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19 After each node's neighbors are hashed to obtain updated node labels, |
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20 a hashed histogram of resulting labels is returned as the final hash. |
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21 |
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22 Hashes are identical for isomorphic graphs and strong guarantees that |
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23 non-isomorphic graphs will get different hashes. See [1] for details. |
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24 |
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25 Note: Similarity between hashes does not imply similarity between graphs. |
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26 |
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27 If no node or edge attributes are provided, the degree of each node |
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28 is used as its initial label. |
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29 Otherwise, node and/or edge labels are used to compute the hash. |
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30 |
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31 Parameters |
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32 ---------- |
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33 G: graph |
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34 The graph to be hashed. |
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35 Can have node and/or edge attributes. Can also have no attributes. |
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36 edge_attr: string |
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37 The key in edge attribute dictionary to be used for hashing. |
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38 If None, edge labels are ignored. |
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39 node_attr: string |
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40 The key in node attribute dictionary to be used for hashing. |
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41 If None, and no edge_attr given, use |
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42 degree of node as label. |
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43 iterations: int |
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44 Number of neighbor aggregations to perform. |
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45 Should be larger for larger graphs. |
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46 digest_size: int |
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47 Size of blake2b hash digest to use for hashing node labels. |
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48 |
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49 Returns |
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50 ------- |
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51 h : string |
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52 Hexadecimal string corresponding to hash of the input graph. |
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53 |
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54 Examples |
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55 -------- |
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56 Two graphs with edge attributes that are isomorphic, except for |
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57 differences in the edge labels. |
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58 |
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59 >>> G1 = nx.Graph() |
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60 >>> G1.add_edges_from( |
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61 ... [ |
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62 ... (1, 2, {"label": "A"}), |
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63 ... (2, 3, {"label": "A"}), |
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64 ... (3, 1, {"label": "A"}), |
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65 ... (1, 4, {"label": "B"}), |
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66 ... ] |
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67 ... ) |
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68 >>> G2 = nx.Graph() |
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69 >>> G2.add_edges_from( |
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70 ... [ |
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71 ... (5, 6, {"label": "B"}), |
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72 ... (6, 7, {"label": "A"}), |
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73 ... (7, 5, {"label": "A"}), |
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74 ... (7, 8, {"label": "A"}), |
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75 ... ] |
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76 ... ) |
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77 |
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78 Omitting the `edge_attr` option, results in identical hashes. |
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79 |
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80 >>> weisfeiler_lehman_graph_hash(G1) |
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81 '0db442538bb6dc81d675bd94e6ebb7ca' |
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82 >>> weisfeiler_lehman_graph_hash(G2) |
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83 '0db442538bb6dc81d675bd94e6ebb7ca' |
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84 |
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85 With edge labels, the graphs are no longer assigned |
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86 the same hash digest. |
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87 |
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88 >>> weisfeiler_lehman_graph_hash(G1, edge_attr="label") |
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89 '408c18537e67d3e56eb7dc92c72cb79e' |
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90 >>> weisfeiler_lehman_graph_hash(G2, edge_attr="label") |
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91 'f9e9cb01c6d2f3b17f83ffeaa24e5986' |
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92 |
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93 References |
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94 ------- |
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95 .. [1] Shervashidze, Nino, Pascal Schweitzer, Erik Jan Van Leeuwen, |
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96 Kurt Mehlhorn, and Karsten M. Borgwardt. Weisfeiler Lehman |
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97 Graph Kernels. Journal of Machine Learning Research. 2011. |
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98 http://www.jmlr.org/papers/volume12/shervashidze11a/shervashidze11a.pdf |
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99 """ |
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100 |
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101 def neighborhood_aggregate(G, node, node_labels, edge_attr=None): |
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102 """ |
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103 Compute new labels for given node by aggregating |
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104 the labels of each node's neighbors. |
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105 """ |
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106 label_list = [node_labels[node]] |
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107 for nei in G.neighbors(node): |
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108 prefix = "" if not edge_attr else G[node][nei][edge_attr] |
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109 label_list.append(prefix + node_labels[nei]) |
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110 return "".join(sorted(label_list)) |
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111 |
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112 def weisfeiler_lehman_step(G, labels, edge_attr=None, node_attr=None): |
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113 """ |
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114 Apply neighborhood aggregation to each node |
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115 in the graph. |
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116 Computes a dictionary with labels for each node. |
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117 """ |
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118 new_labels = dict() |
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119 for node in G.nodes(): |
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120 new_labels[node] = neighborhood_aggregate( |
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121 G, node, labels, edge_attr=edge_attr |
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122 ) |
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123 return new_labels |
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124 |
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125 items = [] |
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126 node_labels = dict() |
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127 # set initial node labels |
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128 for node in G.nodes(): |
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129 if (not node_attr) and (not edge_attr): |
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130 node_labels[node] = str(G.degree(node)) |
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131 elif node_attr: |
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132 node_labels[node] = str(G.nodes[node][node_attr]) |
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133 else: |
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134 node_labels[node] = "" |
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135 |
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136 for k in range(iterations): |
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137 node_labels = weisfeiler_lehman_step(G, node_labels, edge_attr=edge_attr) |
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138 counter = Counter() |
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139 # count node labels |
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140 for node, d in node_labels.items(): |
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141 h = blake2b(digest_size=digest_size) |
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142 h.update(d.encode("ascii")) |
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143 counter.update([h.hexdigest()]) |
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144 # sort the counter, extend total counts |
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145 items.extend(sorted(counter.items(), key=lambda x: x[0])) |
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146 |
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147 # hash the final counter |
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148 h = blake2b(digest_size=digest_size) |
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149 h.update(str(tuple(items)).encode("ascii")) |
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150 h = h.hexdigest() |
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151 return h |