Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/swap.py @ 0:4f3585e2f14b draft default tip
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
author | shellac |
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date | Mon, 22 Mar 2021 18:12:50 +0000 |
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1 """Swap edges in a graph. |
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2 """ |
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3 |
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4 import math |
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5 from networkx.utils import py_random_state |
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6 |
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7 import networkx as nx |
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8 |
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9 __all__ = ["double_edge_swap", "connected_double_edge_swap"] |
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10 |
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11 |
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12 @py_random_state(3) |
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13 def double_edge_swap(G, nswap=1, max_tries=100, seed=None): |
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14 """Swap two edges in the graph while keeping the node degrees fixed. |
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15 |
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16 A double-edge swap removes two randomly chosen edges u-v and x-y |
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17 and creates the new edges u-x and v-y:: |
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18 |
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19 u--v u v |
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20 becomes | | |
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21 x--y x y |
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22 |
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23 If either the edge u-x or v-y already exist no swap is performed |
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24 and another attempt is made to find a suitable edge pair. |
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25 |
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26 Parameters |
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27 ---------- |
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28 G : graph |
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29 An undirected graph |
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30 |
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31 nswap : integer (optional, default=1) |
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32 Number of double-edge swaps to perform |
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33 |
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34 max_tries : integer (optional) |
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35 Maximum number of attempts to swap edges |
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36 |
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37 seed : integer, random_state, or None (default) |
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38 Indicator of random number generation state. |
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39 See :ref:`Randomness<randomness>`. |
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40 |
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41 Returns |
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42 ------- |
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43 G : graph |
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44 The graph after double edge swaps. |
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45 |
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46 Notes |
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47 ----- |
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48 Does not enforce any connectivity constraints. |
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49 |
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50 The graph G is modified in place. |
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51 """ |
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52 if G.is_directed(): |
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53 raise nx.NetworkXError("double_edge_swap() not defined for directed graphs.") |
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54 if nswap > max_tries: |
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55 raise nx.NetworkXError("Number of swaps > number of tries allowed.") |
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56 if len(G) < 4: |
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57 raise nx.NetworkXError("Graph has less than four nodes.") |
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58 # Instead of choosing uniformly at random from a generated edge list, |
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59 # this algorithm chooses nonuniformly from the set of nodes with |
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60 # probability weighted by degree. |
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61 n = 0 |
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62 swapcount = 0 |
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63 keys, degrees = zip(*G.degree()) # keys, degree |
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64 cdf = nx.utils.cumulative_distribution(degrees) # cdf of degree |
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65 discrete_sequence = nx.utils.discrete_sequence |
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66 while swapcount < nswap: |
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67 # if random.random() < 0.5: continue # trick to avoid periodicities? |
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68 # pick two random edges without creating edge list |
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69 # choose source node indices from discrete distribution |
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70 (ui, xi) = discrete_sequence(2, cdistribution=cdf, seed=seed) |
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71 if ui == xi: |
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72 continue # same source, skip |
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73 u = keys[ui] # convert index to label |
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74 x = keys[xi] |
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75 # choose target uniformly from neighbors |
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76 v = seed.choice(list(G[u])) |
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77 y = seed.choice(list(G[x])) |
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78 if v == y: |
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79 continue # same target, skip |
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80 if (x not in G[u]) and (y not in G[v]): # don't create parallel edges |
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81 G.add_edge(u, x) |
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82 G.add_edge(v, y) |
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83 G.remove_edge(u, v) |
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84 G.remove_edge(x, y) |
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85 swapcount += 1 |
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86 if n >= max_tries: |
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87 e = ( |
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88 f"Maximum number of swap attempts ({n}) exceeded " |
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89 f"before desired swaps achieved ({nswap})." |
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90 ) |
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91 raise nx.NetworkXAlgorithmError(e) |
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92 n += 1 |
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93 return G |
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94 |
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95 |
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96 @py_random_state(3) |
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97 def connected_double_edge_swap(G, nswap=1, _window_threshold=3, seed=None): |
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98 """Attempts the specified number of double-edge swaps in the graph `G`. |
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99 |
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100 A double-edge swap removes two randomly chosen edges `(u, v)` and `(x, |
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101 y)` and creates the new edges `(u, x)` and `(v, y)`:: |
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102 |
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103 u--v u v |
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104 becomes | | |
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105 x--y x y |
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106 |
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107 If either `(u, x)` or `(v, y)` already exist, then no swap is performed |
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108 so the actual number of swapped edges is always *at most* `nswap`. |
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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 An undirected graph |
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114 |
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115 nswap : integer (optional, default=1) |
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116 Number of double-edge swaps to perform |
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117 |
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118 _window_threshold : integer |
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119 |
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120 The window size below which connectedness of the graph will be checked |
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121 after each swap. |
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122 |
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123 The "window" in this function is a dynamically updated integer that |
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124 represents the number of swap attempts to make before checking if the |
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125 graph remains connected. It is an optimization used to decrease the |
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126 running time of the algorithm in exchange for increased complexity of |
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127 implementation. |
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128 |
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129 If the window size is below this threshold, then the algorithm checks |
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130 after each swap if the graph remains connected by checking if there is a |
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131 path joining the two nodes whose edge was just removed. If the window |
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132 size is above this threshold, then the algorithm performs do all the |
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133 swaps in the window and only then check if the graph is still connected. |
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134 |
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135 seed : integer, random_state, or None (default) |
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136 Indicator of random number generation state. |
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137 See :ref:`Randomness<randomness>`. |
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138 |
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139 Returns |
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140 ------- |
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141 int |
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142 The number of successful swaps |
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143 |
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144 Raises |
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145 ------ |
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146 |
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147 NetworkXError |
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148 |
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149 If the input graph is not connected, or if the graph has fewer than four |
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150 nodes. |
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151 |
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152 Notes |
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153 ----- |
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154 |
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155 The initial graph `G` must be connected, and the resulting graph is |
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156 connected. The graph `G` is modified in place. |
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157 |
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158 References |
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159 ---------- |
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160 .. [1] C. Gkantsidis and M. Mihail and E. Zegura, |
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161 The Markov chain simulation method for generating connected |
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162 power law random graphs, 2003. |
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163 http://citeseer.ist.psu.edu/gkantsidis03markov.html |
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164 """ |
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165 if not nx.is_connected(G): |
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166 raise nx.NetworkXError("Graph not connected") |
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167 if len(G) < 4: |
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168 raise nx.NetworkXError("Graph has less than four nodes.") |
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169 n = 0 |
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170 swapcount = 0 |
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171 deg = G.degree() |
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172 # Label key for nodes |
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173 dk = list(n for n, d in G.degree()) |
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174 cdf = nx.utils.cumulative_distribution(list(d for n, d in G.degree())) |
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175 discrete_sequence = nx.utils.discrete_sequence |
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176 window = 1 |
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177 while n < nswap: |
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178 wcount = 0 |
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179 swapped = [] |
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180 # If the window is small, we just check each time whether the graph is |
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181 # connected by checking if the nodes that were just separated are still |
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182 # connected. |
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183 if window < _window_threshold: |
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184 # This Boolean keeps track of whether there was a failure or not. |
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185 fail = False |
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186 while wcount < window and n < nswap: |
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187 # Pick two random edges without creating the edge list. Choose |
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188 # source nodes from the discrete degree distribution. |
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189 (ui, xi) = discrete_sequence(2, cdistribution=cdf, seed=seed) |
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190 # If the source nodes are the same, skip this pair. |
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191 if ui == xi: |
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192 continue |
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193 # Convert an index to a node label. |
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194 u = dk[ui] |
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195 x = dk[xi] |
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196 # Choose targets uniformly from neighbors. |
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197 v = seed.choice(list(G.neighbors(u))) |
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198 y = seed.choice(list(G.neighbors(x))) |
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199 # If the target nodes are the same, skip this pair. |
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200 if v == y: |
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201 continue |
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202 if x not in G[u] and y not in G[v]: |
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203 G.remove_edge(u, v) |
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204 G.remove_edge(x, y) |
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205 G.add_edge(u, x) |
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206 G.add_edge(v, y) |
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207 swapped.append((u, v, x, y)) |
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208 swapcount += 1 |
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209 n += 1 |
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210 # If G remains connected... |
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211 if nx.has_path(G, u, v): |
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212 wcount += 1 |
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213 # Otherwise, undo the changes. |
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214 else: |
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215 G.add_edge(u, v) |
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216 G.add_edge(x, y) |
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217 G.remove_edge(u, x) |
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218 G.remove_edge(v, y) |
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219 swapcount -= 1 |
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220 fail = True |
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221 # If one of the swaps failed, reduce the window size. |
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222 if fail: |
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223 window = int(math.ceil(window / 2)) |
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224 else: |
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225 window += 1 |
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226 # If the window is large, then there is a good chance that a bunch of |
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227 # swaps will work. It's quicker to do all those swaps first and then |
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228 # check if the graph remains connected. |
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229 else: |
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230 while wcount < window and n < nswap: |
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231 # Pick two random edges without creating the edge list. Choose |
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232 # source nodes from the discrete degree distribution. |
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233 (ui, xi) = nx.utils.discrete_sequence(2, cdistribution=cdf) |
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234 # If the source nodes are the same, skip this pair. |
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235 if ui == xi: |
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236 continue |
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237 # Convert an index to a node label. |
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238 u = dk[ui] |
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239 x = dk[xi] |
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240 # Choose targets uniformly from neighbors. |
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241 v = seed.choice(list(G.neighbors(u))) |
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242 y = seed.choice(list(G.neighbors(x))) |
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243 # If the target nodes are the same, skip this pair. |
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244 if v == y: |
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245 continue |
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246 if x not in G[u] and y not in G[v]: |
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247 G.remove_edge(u, v) |
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248 G.remove_edge(x, y) |
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249 G.add_edge(u, x) |
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250 G.add_edge(v, y) |
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251 swapped.append((u, v, x, y)) |
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252 swapcount += 1 |
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253 n += 1 |
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254 wcount += 1 |
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255 # If the graph remains connected, increase the window size. |
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256 if nx.is_connected(G): |
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257 window += 1 |
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258 # Otherwise, undo the changes from the previous window and decrease |
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259 # the window size. |
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260 else: |
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261 while swapped: |
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262 (u, v, x, y) = swapped.pop() |
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263 G.add_edge(u, v) |
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264 G.add_edge(x, y) |
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265 G.remove_edge(u, x) |
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266 G.remove_edge(v, y) |
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267 swapcount -= 1 |
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268 window = int(math.ceil(window / 2)) |
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269 return swapcount |