Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/isomorphism/isomorph.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 Graph isomorphism functions. |
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3 """ |
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4 import networkx as nx |
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5 from networkx.exception import NetworkXError |
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6 |
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7 __all__ = [ |
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8 "could_be_isomorphic", |
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9 "fast_could_be_isomorphic", |
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10 "faster_could_be_isomorphic", |
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11 "is_isomorphic", |
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12 ] |
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13 |
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14 |
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15 def could_be_isomorphic(G1, G2): |
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16 """Returns False if graphs are definitely not isomorphic. |
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17 True does NOT guarantee isomorphism. |
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18 |
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19 Parameters |
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20 ---------- |
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21 G1, G2 : graphs |
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22 The two graphs G1 and G2 must be the same type. |
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23 |
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24 Notes |
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25 ----- |
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26 Checks for matching degree, triangle, and number of cliques sequences. |
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27 """ |
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28 |
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29 # Check global properties |
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30 if G1.order() != G2.order(): |
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31 return False |
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32 |
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33 # Check local properties |
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34 d1 = G1.degree() |
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35 t1 = nx.triangles(G1) |
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36 c1 = nx.number_of_cliques(G1) |
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37 props1 = [[d, t1[v], c1[v]] for v, d in d1] |
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38 props1.sort() |
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39 |
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40 d2 = G2.degree() |
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41 t2 = nx.triangles(G2) |
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42 c2 = nx.number_of_cliques(G2) |
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43 props2 = [[d, t2[v], c2[v]] for v, d in d2] |
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44 props2.sort() |
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45 |
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46 if props1 != props2: |
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47 return False |
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48 |
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49 # OK... |
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50 return True |
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51 |
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52 |
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53 graph_could_be_isomorphic = could_be_isomorphic |
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54 |
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55 |
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56 def fast_could_be_isomorphic(G1, G2): |
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57 """Returns False if graphs are definitely not isomorphic. |
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58 |
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59 True does NOT guarantee isomorphism. |
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60 |
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61 Parameters |
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62 ---------- |
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63 G1, G2 : graphs |
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64 The two graphs G1 and G2 must be the same type. |
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65 |
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66 Notes |
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67 ----- |
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68 Checks for matching degree and triangle sequences. |
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69 """ |
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70 # Check global properties |
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71 if G1.order() != G2.order(): |
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72 return False |
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73 |
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74 # Check local properties |
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75 d1 = G1.degree() |
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76 t1 = nx.triangles(G1) |
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77 props1 = [[d, t1[v]] for v, d in d1] |
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78 props1.sort() |
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79 |
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80 d2 = G2.degree() |
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81 t2 = nx.triangles(G2) |
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82 props2 = [[d, t2[v]] for v, d in d2] |
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83 props2.sort() |
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84 |
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85 if props1 != props2: |
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86 return False |
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87 |
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88 # OK... |
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89 return True |
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90 |
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91 |
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92 fast_graph_could_be_isomorphic = fast_could_be_isomorphic |
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93 |
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94 |
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95 def faster_could_be_isomorphic(G1, G2): |
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96 """Returns False if graphs are definitely not isomorphic. |
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97 |
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98 True does NOT guarantee isomorphism. |
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99 |
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100 Parameters |
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101 ---------- |
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102 G1, G2 : graphs |
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103 The two graphs G1 and G2 must be the same type. |
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104 |
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105 Notes |
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106 ----- |
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107 Checks for matching degree sequences. |
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108 """ |
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109 # Check global properties |
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110 if G1.order() != G2.order(): |
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111 return False |
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112 |
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113 # Check local properties |
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114 d1 = sorted(d for n, d in G1.degree()) |
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115 d2 = sorted(d for n, d in G2.degree()) |
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116 |
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117 if d1 != d2: |
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118 return False |
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119 |
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120 # OK... |
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121 return True |
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122 |
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123 |
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124 faster_graph_could_be_isomorphic = faster_could_be_isomorphic |
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125 |
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126 |
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127 def is_isomorphic(G1, G2, node_match=None, edge_match=None): |
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128 """Returns True if the graphs G1 and G2 are isomorphic and False otherwise. |
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129 |
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130 Parameters |
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131 ---------- |
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132 G1, G2: graphs |
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133 The two graphs G1 and G2 must be the same type. |
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134 |
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135 node_match : callable |
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136 A function that returns True if node n1 in G1 and n2 in G2 should |
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137 be considered equal during the isomorphism test. |
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138 If node_match is not specified then node attributes are not considered. |
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139 |
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140 The function will be called like |
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141 |
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142 node_match(G1.nodes[n1], G2.nodes[n2]). |
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143 |
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144 That is, the function will receive the node attribute dictionaries |
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145 for n1 and n2 as inputs. |
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146 |
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147 edge_match : callable |
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148 A function that returns True if the edge attribute dictionary |
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149 for the pair of nodes (u1, v1) in G1 and (u2, v2) in G2 should |
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150 be considered equal during the isomorphism test. If edge_match is |
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151 not specified then edge attributes are not considered. |
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152 |
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153 The function will be called like |
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154 |
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155 edge_match(G1[u1][v1], G2[u2][v2]). |
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156 |
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157 That is, the function will receive the edge attribute dictionaries |
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158 of the edges under consideration. |
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159 |
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160 Notes |
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161 ----- |
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162 Uses the vf2 algorithm [1]_. |
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163 |
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164 Examples |
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165 -------- |
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166 >>> import networkx.algorithms.isomorphism as iso |
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167 |
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168 For digraphs G1 and G2, using 'weight' edge attribute (default: 1) |
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169 |
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170 >>> G1 = nx.DiGraph() |
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171 >>> G2 = nx.DiGraph() |
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172 >>> nx.add_path(G1, [1, 2, 3, 4], weight=1) |
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173 >>> nx.add_path(G2, [10, 20, 30, 40], weight=2) |
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174 >>> em = iso.numerical_edge_match("weight", 1) |
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175 >>> nx.is_isomorphic(G1, G2) # no weights considered |
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176 True |
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177 >>> nx.is_isomorphic(G1, G2, edge_match=em) # match weights |
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178 False |
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179 |
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180 For multidigraphs G1 and G2, using 'fill' node attribute (default: '') |
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181 |
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182 >>> G1 = nx.MultiDiGraph() |
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183 >>> G2 = nx.MultiDiGraph() |
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184 >>> G1.add_nodes_from([1, 2, 3], fill="red") |
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185 >>> G2.add_nodes_from([10, 20, 30, 40], fill="red") |
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186 >>> nx.add_path(G1, [1, 2, 3, 4], weight=3, linewidth=2.5) |
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187 >>> nx.add_path(G2, [10, 20, 30, 40], weight=3) |
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188 >>> nm = iso.categorical_node_match("fill", "red") |
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189 >>> nx.is_isomorphic(G1, G2, node_match=nm) |
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190 True |
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191 |
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192 For multidigraphs G1 and G2, using 'weight' edge attribute (default: 7) |
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193 |
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194 >>> G1.add_edge(1, 2, weight=7) |
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195 1 |
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196 >>> G2.add_edge(10, 20) |
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197 1 |
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198 >>> em = iso.numerical_multiedge_match("weight", 7, rtol=1e-6) |
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199 >>> nx.is_isomorphic(G1, G2, edge_match=em) |
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200 True |
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201 |
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202 For multigraphs G1 and G2, using 'weight' and 'linewidth' edge attributes |
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203 with default values 7 and 2.5. Also using 'fill' node attribute with |
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204 default value 'red'. |
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205 |
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206 >>> em = iso.numerical_multiedge_match(["weight", "linewidth"], [7, 2.5]) |
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207 >>> nm = iso.categorical_node_match("fill", "red") |
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208 >>> nx.is_isomorphic(G1, G2, edge_match=em, node_match=nm) |
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209 True |
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210 |
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211 See Also |
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212 -------- |
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213 numerical_node_match, numerical_edge_match, numerical_multiedge_match |
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214 categorical_node_match, categorical_edge_match, categorical_multiedge_match |
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215 |
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216 References |
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217 ---------- |
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218 .. [1] L. P. Cordella, P. Foggia, C. Sansone, M. Vento, |
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219 "An Improved Algorithm for Matching Large Graphs", |
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220 3rd IAPR-TC15 Workshop on Graph-based Representations in |
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221 Pattern Recognition, Cuen, pp. 149-159, 2001. |
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222 http://amalfi.dis.unina.it/graph/db/papers/vf-algorithm.pdf |
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223 """ |
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224 if G1.is_directed() and G2.is_directed(): |
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225 GM = nx.algorithms.isomorphism.DiGraphMatcher |
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226 elif (not G1.is_directed()) and (not G2.is_directed()): |
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227 GM = nx.algorithms.isomorphism.GraphMatcher |
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228 else: |
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229 raise NetworkXError("Graphs G1 and G2 are not of the same type.") |
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230 |
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231 gm = GM(G1, G2, node_match=node_match, edge_match=edge_match) |
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232 |
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233 return gm.is_isomorphic() |