Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/sitepackages/networkx/algorithms/isomorphism/temporalisomorphvf2.py @ 0:4f3585e2f14b draft default tip
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author  shellac 

date  Mon, 22 Mar 2021 18:12:50 +0000 
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1 """ 
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2 ***************************** 
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3 Timerespecting VF2 Algorithm 
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4 ***************************** 
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5 
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6 An extension of the VF2 algorithm for timerespecting graph ismorphism 
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7 testing in temporal graphs. 
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8 
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9 A temporal graph is one in which edges contain a datetime attribute, 
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10 denoting when interaction occurred between the incident nodes. A 
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11 timerespecting subgraph of a temporal graph is a subgraph such that 
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12 all interactions incident to a node occurred within a time threshold, 
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13 delta, of each other. A directed timerespecting subgraph has the 
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14 added constraint that incoming interactions to a node must precede 
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15 outgoing interactions from the same node  this enforces a sense of 
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16 directed flow. 
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17 
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18 Introduction 
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19  
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20 
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21 The TimeRespectingGraphMatcher and TimeRespectingDiGraphMatcher 
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22 extend the GraphMatcher and DiGraphMatcher classes, respectively, 
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23 to include temporal constraints on matches. This is achieved through 
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24 a semantic check, via the semantic_feasibility() function. 
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25 
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26 As well as including G1 (the graph in which to seek embeddings) and 
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27 G2 (the subgraph structure of interest), the name of the temporal 
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28 attribute on the edges and the time threshold, delta, must be supplied 
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29 as arguments to the matching constructors. 
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30 
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31 A delta of zero is the strictest temporal constraint on the match  
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32 only embeddings in which all interactions occur at the same time will 
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33 be returned. A delta of one day will allow embeddings in which 
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34 adjacent interactions occur up to a day apart. 
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35 
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36 Examples 
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37  
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38 
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39 Examples will be provided when the datetime type has been incorporated. 
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40 
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41 
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42 Temporal Subgraph Isomorphism 
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43  
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44 
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45 A brief discussion of the somewhat diverse current literature will be 
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46 included here. 
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47 
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48 References 
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49  
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50 
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51 [1] Redmond, U. and Cunningham, P. Temporal subgraph isomorphism. In: 
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52 The 2013 IEEE/ACM International Conference on Advances in Social 
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53 Networks Analysis and Mining (ASONAM). Niagara Falls, Canada; 2013: 
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54 pages 1451  1452. [65] 
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55 
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56 For a discussion of the literature on temporal networks: 
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57 
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58 [3] P. Holme and J. Saramaki. Temporal networks. Physics Reports, 
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59 519(3):97–125, 2012. 
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60 
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61 Notes 
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62  
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63 
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64 Handles directed and undirected graphs and graphs with parallel edges. 
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65 
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66 """ 
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67 
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68 import networkx as nx 
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69 from .isomorphvf2 import GraphMatcher, DiGraphMatcher 
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70 
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71 __all__ = ["TimeRespectingGraphMatcher", "TimeRespectingDiGraphMatcher"] 
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72 
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73 
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74 class TimeRespectingGraphMatcher(GraphMatcher): 
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75 def __init__(self, G1, G2, temporal_attribute_name, delta): 
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76 """Initialize TimeRespectingGraphMatcher. 
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77 
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78 G1 and G2 should be nx.Graph or nx.MultiGraph instances. 
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79 
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80 Examples 
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81  
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82 To create a TimeRespectingGraphMatcher which checks for 
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83 syntactic and semantic feasibility: 
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84 
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85 >>> from networkx.algorithms import isomorphism 
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86 >>> from datetime import timedelta 
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87 >>> G1 = nx.Graph(nx.path_graph(4, create_using=nx.Graph())) 
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88 
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89 >>> G2 = nx.Graph(nx.path_graph(4, create_using=nx.Graph())) 
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90 
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91 >>> GM = isomorphism.TimeRespectingGraphMatcher( 
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92 ... G1, G2, "date", timedelta(days=1) 
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93 ... ) 
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94 """ 
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95 self.temporal_attribute_name = temporal_attribute_name 
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96 self.delta = delta 
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97 super().__init__(G1, G2) 
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98 
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99 def one_hop(self, Gx, Gx_node, neighbors): 
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100 """ 
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101 Edges one hop out from a node in the mapping should be 
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102 timerespecting with respect to each other. 
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103 """ 
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104 dates = [] 
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105 for n in neighbors: 
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106 if isinstance(Gx, nx.Graph): # Graph G[u][v] returns the data dictionary. 
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107 dates.append(Gx[Gx_node][n][self.temporal_attribute_name]) 
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108 else: # MultiGraph G[u][v] returns a dictionary of key > data dictionary. 
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109 for edge in Gx[Gx_node][ 
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110 n 
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111 ].values(): # Iterates all edges between node pair. 
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112 dates.append(edge[self.temporal_attribute_name]) 
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113 if any(x is None for x in dates): 
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114 raise ValueError("Datetime not supplied for at least one edge.") 
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115 return not dates or max(dates)  min(dates) <= self.delta 
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116 
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117 def two_hop(self, Gx, core_x, Gx_node, neighbors): 
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118 """ 
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119 Paths of length 2 from Gx_node should be timerespecting. 
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120 """ 
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121 return all( 
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122 self.one_hop(Gx, v, [n for n in Gx[v] if n in core_x] + [Gx_node]) 
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123 for v in neighbors 
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124 ) 
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125 
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126 def semantic_feasibility(self, G1_node, G2_node): 
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127 """Returns True if adding (G1_node, G2_node) is semantically 
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128 feasible. 
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129 
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130 Any subclass which redefines semantic_feasibility() must 
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131 maintain the self.tests if needed, to keep the match() method 
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132 functional. Implementations should consider multigraphs. 
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133 """ 
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134 neighbors = [n for n in self.G1[G1_node] if n in self.core_1] 
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135 if not self.one_hop(self.G1, G1_node, neighbors): # Fail fast on first node. 
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136 return False 
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137 if not self.two_hop(self.G1, self.core_1, G1_node, neighbors): 
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138 return False 
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139 # Otherwise, this node is semantically feasible! 
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140 return True 
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141 
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142 
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143 class TimeRespectingDiGraphMatcher(DiGraphMatcher): 
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144 def __init__(self, G1, G2, temporal_attribute_name, delta): 
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145 """Initialize TimeRespectingDiGraphMatcher. 
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146 
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147 G1 and G2 should be nx.DiGraph or nx.MultiDiGraph instances. 
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148 
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149 Examples 
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150  
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151 To create a TimeRespectingDiGraphMatcher which checks for 
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152 syntactic and semantic feasibility: 
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153 
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154 >>> from networkx.algorithms import isomorphism 
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155 >>> from datetime import timedelta 
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156 >>> G1 = nx.DiGraph(nx.path_graph(4, create_using=nx.DiGraph())) 
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157 
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158 >>> G2 = nx.DiGraph(nx.path_graph(4, create_using=nx.DiGraph())) 
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159 
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160 >>> GM = isomorphism.TimeRespectingDiGraphMatcher( 
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161 ... G1, G2, "date", timedelta(days=1) 
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162 ... ) 
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163 """ 
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164 self.temporal_attribute_name = temporal_attribute_name 
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165 self.delta = delta 
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166 super().__init__(G1, G2) 
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167 
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168 def get_pred_dates(self, Gx, Gx_node, core_x, pred): 
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169 """ 
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170 Get the dates of edges from predecessors. 
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171 """ 
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172 pred_dates = [] 
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173 if isinstance(Gx, nx.DiGraph): # Graph G[u][v] returns the data dictionary. 
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174 for n in pred: 
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175 pred_dates.append(Gx[n][Gx_node][self.temporal_attribute_name]) 
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176 else: # MultiGraph G[u][v] returns a dictionary of key > data dictionary. 
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177 for n in pred: 
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178 for edge in Gx[n][ 
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179 Gx_node 
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180 ].values(): # Iterates all edge data between node pair. 
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181 pred_dates.append(edge[self.temporal_attribute_name]) 
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182 return pred_dates 
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183 
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184 def get_succ_dates(self, Gx, Gx_node, core_x, succ): 
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185 """ 
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186 Get the dates of edges to successors. 
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187 """ 
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188 succ_dates = [] 
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189 if isinstance(Gx, nx.DiGraph): # Graph G[u][v] returns the data dictionary. 
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190 for n in succ: 
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191 succ_dates.append(Gx[Gx_node][n][self.temporal_attribute_name]) 
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192 else: # MultiGraph G[u][v] returns a dictionary of key > data dictionary. 
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193 for n in succ: 
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194 for edge in Gx[Gx_node][ 
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195 n 
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196 ].values(): # Iterates all edge data between node pair. 
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197 succ_dates.append(edge[self.temporal_attribute_name]) 
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198 return succ_dates 
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199 
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200 def one_hop(self, Gx, Gx_node, core_x, pred, succ): 
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201 """ 
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202 The ego node. 
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203 """ 
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204 pred_dates = self.get_pred_dates(Gx, Gx_node, core_x, pred) 
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205 succ_dates = self.get_succ_dates(Gx, Gx_node, core_x, succ) 
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206 return self.test_one(pred_dates, succ_dates) and self.test_two( 
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207 pred_dates, succ_dates 
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208 ) 
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209 
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210 def two_hop_pred(self, Gx, Gx_node, core_x, pred): 
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211 """ 
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212 The predeccessors of the ego node. 
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213 """ 
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214 return all( 
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215 self.one_hop( 
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216 Gx, 
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217 p, 
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218 core_x, 
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219 self.preds(Gx, core_x, p), 
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220 self.succs(Gx, core_x, p, Gx_node), 
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221 ) 
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222 for p in pred 
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223 ) 
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224 
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225 def two_hop_succ(self, Gx, Gx_node, core_x, succ): 
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226 """ 
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227 The successors of the ego node. 
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228 """ 
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229 return all( 
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230 self.one_hop( 
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231 Gx, 
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232 s, 
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233 core_x, 
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234 self.preds(Gx, core_x, s, Gx_node), 
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235 self.succs(Gx, core_x, s), 
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236 ) 
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237 for s in succ 
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238 ) 
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239 
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240 def preds(self, Gx, core_x, v, Gx_node=None): 
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241 pred = [n for n in Gx.predecessors(v) if n in core_x] 
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242 if Gx_node: 
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243 pred.append(Gx_node) 
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244 return pred 
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245 
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246 def succs(self, Gx, core_x, v, Gx_node=None): 
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247 succ = [n for n in Gx.successors(v) if n in core_x] 
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248 if Gx_node: 
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249 succ.append(Gx_node) 
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250 return succ 
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251 
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252 def test_one(self, pred_dates, succ_dates): 
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253 """ 
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254 Edges one hop out from Gx_node in the mapping should be 
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255 timerespecting with respect to each other, regardless of 
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256 direction. 
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257 """ 
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258 time_respecting = True 
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259 dates = pred_dates + succ_dates 
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260 
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261 if any(x is None for x in dates): 
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262 raise ValueError("Date or datetime not supplied for at least one edge.") 
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263 
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264 dates.sort() # Small to large. 
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265 if 0 < len(dates) and not (dates[1]  dates[0] <= self.delta): 
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266 time_respecting = False 
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267 return time_respecting 
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268 
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269 def test_two(self, pred_dates, succ_dates): 
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270 """ 
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271 Edges from a dual Gx_node in the mapping should be ordered in 
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272 a timerespecting manner. 
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273 """ 
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274 time_respecting = True 
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275 pred_dates.sort() 
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276 succ_dates.sort() 
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277 # First out before last in; negative of the necessary condition for timerespect. 
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278 if ( 
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279 0 < len(succ_dates) 
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280 and 0 < len(pred_dates) 
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281 and succ_dates[0] < pred_dates[1] 
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282 ): 
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283 time_respecting = False 
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284 return time_respecting 
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285 
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286 def semantic_feasibility(self, G1_node, G2_node): 
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287 """Returns True if adding (G1_node, G2_node) is semantically 
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288 feasible. 
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289 
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290 Any subclass which redefines semantic_feasibility() must 
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291 maintain the self.tests if needed, to keep the match() method 
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292 functional. Implementations should consider multigraphs. 
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293 """ 
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294 pred, succ = ( 
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295 [n for n in self.G1.predecessors(G1_node) if n in self.core_1], 
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296 [n for n in self.G1.successors(G1_node) if n in self.core_1], 
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297 ) 
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298 if not self.one_hop( 
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299 self.G1, G1_node, self.core_1, pred, succ 
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300 ): # Fail fast on first node. 
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301 return False 
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302 if not self.two_hop_pred(self.G1, G1_node, self.core_1, pred): 
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303 return False 
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304 if not self.two_hop_succ(self.G1, G1_node, self.core_1, succ): 
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305 return False 
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306 # Otherwise, this node is semantically feasible! 
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307 return True 