Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/regular.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 """Functions for computing and verifying regular graphs.""" |
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2 import networkx as nx |
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3 from networkx.utils import not_implemented_for |
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4 |
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5 __all__ = ["is_regular", "is_k_regular", "k_factor"] |
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6 |
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7 |
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8 def is_regular(G): |
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9 """Determines whether the graph ``G`` is a regular graph. |
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10 |
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11 A regular graph is a graph where each vertex has the same degree. A |
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12 regular digraph is a graph where the indegree and outdegree of each |
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13 vertex are equal. |
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14 |
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15 Parameters |
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16 ---------- |
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17 G : NetworkX graph |
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18 |
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19 Returns |
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20 ------- |
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21 bool |
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22 Whether the given graph or digraph is regular. |
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23 |
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24 """ |
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25 n1 = nx.utils.arbitrary_element(G) |
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26 if not G.is_directed(): |
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27 d1 = G.degree(n1) |
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28 return all(d1 == d for _, d in G.degree) |
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29 else: |
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30 d_in = G.in_degree(n1) |
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31 in_regular = all(d_in == d for _, d in G.in_degree) |
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32 d_out = G.out_degree(n1) |
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33 out_regular = all(d_out == d for _, d in G.out_degree) |
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34 return in_regular and out_regular |
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35 |
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36 |
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37 @not_implemented_for("directed") |
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38 def is_k_regular(G, k): |
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39 """Determines whether the graph ``G`` is a k-regular graph. |
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40 |
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41 A k-regular graph is a graph where each vertex has degree k. |
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42 |
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43 Parameters |
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44 ---------- |
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45 G : NetworkX graph |
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46 |
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47 Returns |
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48 ------- |
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49 bool |
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50 Whether the given graph is k-regular. |
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51 |
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52 """ |
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53 return all(d == k for n, d in G.degree) |
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54 |
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55 |
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56 @not_implemented_for("directed") |
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57 @not_implemented_for("multigraph") |
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58 def k_factor(G, k, matching_weight="weight"): |
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59 """Compute a k-factor of G |
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60 |
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61 A k-factor of a graph is a spanning k-regular subgraph. |
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62 A spanning k-regular subgraph of G is a subgraph that contains |
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63 each vertex of G and a subset of the edges of G such that each |
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64 vertex has degree k. |
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65 |
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66 Parameters |
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67 ---------- |
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68 G : NetworkX graph |
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69 Undirected graph |
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70 |
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71 weight: string, optional (default='weight') |
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72 Edge data key corresponding to the edge weight. |
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73 Used for finding the max-weighted perfect matching. |
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74 If key not found, uses 1 as weight. |
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75 |
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76 Returns |
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77 ------- |
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78 G2 : NetworkX graph |
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79 A k-factor of G |
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80 |
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81 References |
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82 ---------- |
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83 .. [1] "An algorithm for computing simple k-factors.", |
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84 Meijer, Henk, Yurai Núñez-RodrÃguez, and David Rappaport, |
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85 Information processing letters, 2009. |
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86 """ |
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87 |
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88 from networkx.algorithms.matching import max_weight_matching |
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89 from networkx.algorithms.matching import is_perfect_matching |
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90 |
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91 class LargeKGadget: |
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92 def __init__(self, k, degree, node, g): |
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93 self.original = node |
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94 self.g = g |
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95 self.k = k |
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96 self.degree = degree |
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97 |
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98 self.outer_vertices = [(node, x) for x in range(degree)] |
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99 self.core_vertices = [(node, x + degree) for x in range(degree - k)] |
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100 |
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101 def replace_node(self): |
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102 adj_view = self.g[self.original] |
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103 neighbors = list(adj_view.keys()) |
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104 edge_attrs = list(adj_view.values()) |
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105 for (outer, neighbor, edge_attrs) in zip( |
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106 self.outer_vertices, neighbors, edge_attrs |
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107 ): |
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108 self.g.add_edge(outer, neighbor, **edge_attrs) |
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109 for core in self.core_vertices: |
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110 for outer in self.outer_vertices: |
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111 self.g.add_edge(core, outer) |
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112 self.g.remove_node(self.original) |
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113 |
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114 def restore_node(self): |
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115 self.g.add_node(self.original) |
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116 for outer in self.outer_vertices: |
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117 adj_view = self.g[outer] |
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118 for neighbor, edge_attrs in list(adj_view.items()): |
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119 if neighbor not in self.core_vertices: |
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120 self.g.add_edge(self.original, neighbor, **edge_attrs) |
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121 break |
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122 g.remove_nodes_from(self.outer_vertices) |
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123 g.remove_nodes_from(self.core_vertices) |
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124 |
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125 class SmallKGadget: |
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126 def __init__(self, k, degree, node, g): |
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127 self.original = node |
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128 self.k = k |
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129 self.degree = degree |
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130 self.g = g |
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131 |
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132 self.outer_vertices = [(node, x) for x in range(degree)] |
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133 self.inner_vertices = [(node, x + degree) for x in range(degree)] |
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134 self.core_vertices = [(node, x + 2 * degree) for x in range(k)] |
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135 |
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136 def replace_node(self): |
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137 adj_view = self.g[self.original] |
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138 for (outer, inner, (neighbor, edge_attrs)) in zip( |
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139 self.outer_vertices, self.inner_vertices, list(adj_view.items()) |
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140 ): |
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141 self.g.add_edge(outer, inner) |
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142 self.g.add_edge(outer, neighbor, **edge_attrs) |
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143 for core in self.core_vertices: |
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144 for inner in self.inner_vertices: |
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145 self.g.add_edge(core, inner) |
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146 self.g.remove_node(self.original) |
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147 |
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148 def restore_node(self): |
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149 self.g.add_node(self.original) |
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150 for outer in self.outer_vertices: |
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151 adj_view = self.g[outer] |
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152 for neighbor, edge_attrs in adj_view.items(): |
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153 if neighbor not in self.core_vertices: |
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154 self.g.add_edge(self.original, neighbor, **edge_attrs) |
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155 break |
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156 self.g.remove_nodes_from(self.outer_vertices) |
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157 self.g.remove_nodes_from(self.inner_vertices) |
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158 self.g.remove_nodes_from(self.core_vertices) |
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159 |
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160 # Step 1 |
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161 if any(d < k for _, d in G.degree): |
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162 raise nx.NetworkXUnfeasible("Graph contains a vertex with degree less than k") |
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163 g = G.copy() |
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164 |
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165 # Step 2 |
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166 gadgets = [] |
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167 for node, degree in list(g.degree): |
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168 if k < degree / 2.0: |
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169 gadget = SmallKGadget(k, degree, node, g) |
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170 else: |
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171 gadget = LargeKGadget(k, degree, node, g) |
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172 gadget.replace_node() |
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173 gadgets.append(gadget) |
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174 |
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175 # Step 3 |
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176 matching = max_weight_matching(g, maxcardinality=True, weight=matching_weight) |
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177 |
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178 # Step 4 |
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179 if not is_perfect_matching(g, matching): |
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180 raise nx.NetworkXUnfeasible( |
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181 "Cannot find k-factor because no perfect matching exists" |
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182 ) |
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183 |
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184 for edge in g.edges(): |
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185 if edge not in matching and (edge[1], edge[0]) not in matching: |
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186 g.remove_edge(edge[0], edge[1]) |
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187 |
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188 for gadget in gadgets: |
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189 gadget.restore_node() |
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190 |
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191 return g |