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annotate planemo/lib/python3.7/site-packages/networkx/algorithms/swap.py @ 1:56ad4e20f292 draft

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"planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
author guerler
date Fri, 31 Jul 2020 00:32:28 -0400
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1 # -*- coding: utf-8 -*-
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2 """Swap edges in a graph.
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3 """
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4 # Copyright (C) 2004-2019 by
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5 # Aric Hagberg <hagberg@lanl.gov>
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6 # Dan Schult <dschult@colgate.edu>
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7 # Pieter Swart <swart@lanl.gov>
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8 # All rights reserved.
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9 # BSD license.
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10
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11 import math
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12 from networkx.utils import py_random_state
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13
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14 import networkx as nx
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15
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16 __author__ = "\n".join(['Aric Hagberg (hagberg@lanl.gov)',
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17 'Pieter Swart (swart@lanl.gov)',
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18 'Dan Schult (dschult@colgate.edu)',
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19 'Joel Miller (joel.c.miller.research@gmail.com)',
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20 'Ben Edwards'])
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21
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22 __all__ = ['double_edge_swap',
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23 'connected_double_edge_swap']
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24
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25
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26 @py_random_state(3)
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27 def double_edge_swap(G, nswap=1, max_tries=100, seed=None):
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28 """Swap two edges in the graph while keeping the node degrees fixed.
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29
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30 A double-edge swap removes two randomly chosen edges u-v and x-y
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31 and creates the new edges u-x and v-y::
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32
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33 u--v u v
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34 becomes | |
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35 x--y x y
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36
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37 If either the edge u-x or v-y already exist no swap is performed
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38 and another attempt is made to find a suitable edge pair.
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39
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40 Parameters
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41 ----------
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42 G : graph
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43 An undirected graph
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44
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45 nswap : integer (optional, default=1)
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46 Number of double-edge swaps to perform
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47
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48 max_tries : integer (optional)
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49 Maximum number of attempts to swap edges
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50
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51 seed : integer, random_state, or None (default)
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52 Indicator of random number generation state.
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53 See :ref:`Randomness<randomness>`.
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54
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55 Returns
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56 -------
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57 G : graph
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58 The graph after double edge swaps.
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59
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60 Notes
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61 -----
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62 Does not enforce any connectivity constraints.
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63
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64 The graph G is modified in place.
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65 """
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66 if G.is_directed():
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67 raise nx.NetworkXError(
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68 "double_edge_swap() not defined for directed graphs.")
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69 if nswap > max_tries:
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70 raise nx.NetworkXError("Number of swaps > number of tries allowed.")
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71 if len(G) < 4:
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72 raise nx.NetworkXError("Graph has less than four nodes.")
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73 # Instead of choosing uniformly at random from a generated edge list,
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74 # this algorithm chooses nonuniformly from the set of nodes with
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75 # probability weighted by degree.
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76 n = 0
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77 swapcount = 0
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78 keys, degrees = zip(*G.degree()) # keys, degree
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79 cdf = nx.utils.cumulative_distribution(degrees) # cdf of degree
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80 discrete_sequence = nx.utils.discrete_sequence
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81 while swapcount < nswap:
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82 # if random.random() < 0.5: continue # trick to avoid periodicities?
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83 # pick two random edges without creating edge list
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84 # choose source node indices from discrete distribution
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85 (ui, xi) = discrete_sequence(2, cdistribution=cdf, seed=seed)
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86 if ui == xi:
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87 continue # same source, skip
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88 u = keys[ui] # convert index to label
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89 x = keys[xi]
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90 # choose target uniformly from neighbors
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91 v = seed.choice(list(G[u]))
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92 y = seed.choice(list(G[x]))
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93 if v == y:
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94 continue # same target, skip
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95 if (x not in G[u]) and (y not in G[v]): # don't create parallel edges
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96 G.add_edge(u, x)
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97 G.add_edge(v, y)
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98 G.remove_edge(u, v)
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99 G.remove_edge(x, y)
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100 swapcount += 1
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101 if n >= max_tries:
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102 e = ('Maximum number of swap attempts (%s) exceeded ' % n +
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103 'before desired swaps achieved (%s).' % nswap)
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104 raise nx.NetworkXAlgorithmError(e)
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105 n += 1
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106 return G
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107
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108
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109 @py_random_state(3)
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110 def connected_double_edge_swap(G, nswap=1, _window_threshold=3, seed=None):
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111 """Attempts the specified number of double-edge swaps in the graph `G`.
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112
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113 A double-edge swap removes two randomly chosen edges `(u, v)` and `(x,
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114 y)` and creates the new edges `(u, x)` and `(v, y)`::
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115
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116 u--v u v
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117 becomes | |
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118 x--y x y
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119
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120 If either `(u, x)` or `(v, y)` already exist, then no swap is performed
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121 so the actual number of swapped edges is always *at most* `nswap`.
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122
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123 Parameters
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124 ----------
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125 G : graph
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126 An undirected graph
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127
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128 nswap : integer (optional, default=1)
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129 Number of double-edge swaps to perform
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130
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131 _window_threshold : integer
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132
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133 The window size below which connectedness of the graph will be checked
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134 after each swap.
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135
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136 The "window" in this function is a dynamically updated integer that
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137 represents the number of swap attempts to make before checking if the
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138 graph remains connected. It is an optimization used to decrease the
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139 running time of the algorithm in exchange for increased complexity of
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140 implementation.
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141
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142 If the window size is below this threshold, then the algorithm checks
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143 after each swap if the graph remains connected by checking if there is a
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144 path joining the two nodes whose edge was just removed. If the window
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145 size is above this threshold, then the algorithm performs do all the
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146 swaps in the window and only then check if the graph is still connected.
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147
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148 seed : integer, random_state, or None (default)
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149 Indicator of random number generation state.
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150 See :ref:`Randomness<randomness>`.
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151
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152 Returns
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153 -------
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154 int
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155 The number of successful swaps
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156
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157 Raises
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158 ------
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159
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160 NetworkXError
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161
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162 If the input graph is not connected, or if the graph has fewer than four
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163 nodes.
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164
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165 Notes
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166 -----
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167
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168 The initial graph `G` must be connected, and the resulting graph is
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169 connected. The graph `G` is modified in place.
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170
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171 References
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172 ----------
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173 .. [1] C. Gkantsidis and M. Mihail and E. Zegura,
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174 The Markov chain simulation method for generating connected
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175 power law random graphs, 2003.
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176 http://citeseer.ist.psu.edu/gkantsidis03markov.html
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177 """
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178 if not nx.is_connected(G):
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179 raise nx.NetworkXError("Graph not connected")
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180 if len(G) < 4:
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181 raise nx.NetworkXError("Graph has less than four nodes.")
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182 n = 0
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183 swapcount = 0
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184 deg = G.degree()
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185 # Label key for nodes
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186 dk = list(n for n, d in G.degree())
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187 cdf = nx.utils.cumulative_distribution(list(d for n, d in G.degree()))
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188 discrete_sequence = nx.utils.discrete_sequence
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189 window = 1
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190 while n < nswap:
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191 wcount = 0
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192 swapped = []
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193 # If the window is small, we just check each time whether the graph is
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194 # connected by checking if the nodes that were just separated are still
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195 # connected.
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196 if window < _window_threshold:
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197 # This Boolean keeps track of whether there was a failure or not.
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198 fail = False
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199 while wcount < window and n < nswap:
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200 # Pick two random edges without creating the edge list. Choose
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201 # source nodes from the discrete degree distribution.
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202 (ui, xi) = discrete_sequence(2, cdistribution=cdf, seed=seed)
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203 # If the source nodes are the same, skip this pair.
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204 if ui == xi:
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205 continue
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206 # Convert an index to a node label.
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207 u = dk[ui]
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208 x = dk[xi]
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209 # Choose targets uniformly from neighbors.
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210 v = seed.choice(list(G.neighbors(u)))
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211 y = seed.choice(list(G.neighbors(x)))
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212 # If the target nodes are the same, skip this pair.
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213 if v == y:
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214 continue
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215 if x not in G[u] and y not in G[v]:
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216 G.remove_edge(u, v)
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217 G.remove_edge(x, y)
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218 G.add_edge(u, x)
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219 G.add_edge(v, y)
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220 swapped.append((u, v, x, y))
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221 swapcount += 1
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222 n += 1
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223 # If G remains connected...
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224 if nx.has_path(G, u, v):
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225 wcount += 1
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226 # Otherwise, undo the changes.
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227 else:
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228 G.add_edge(u, v)
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229 G.add_edge(x, y)
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230 G.remove_edge(u, x)
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231 G.remove_edge(v, y)
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232 swapcount -= 1
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233 fail = True
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234 # If one of the swaps failed, reduce the window size.
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235 if fail:
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236 window = int(math.ceil(window / 2))
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237 else:
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238 window += 1
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239 # If the window is large, then there is a good chance that a bunch of
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240 # swaps will work. It's quicker to do all those swaps first and then
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241 # check if the graph remains connected.
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242 else:
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243 while wcount < window and n < nswap:
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244 # Pick two random edges without creating the edge list. Choose
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245 # source nodes from the discrete degree distribution.
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246 (ui, xi) = nx.utils.discrete_sequence(2, cdistribution=cdf)
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247 # If the source nodes are the same, skip this pair.
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248 if ui == xi:
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249 continue
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250 # Convert an index to a node label.
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251 u = dk[ui]
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252 x = dk[xi]
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253 # Choose targets uniformly from neighbors.
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254 v = seed.choice(list(G.neighbors(u)))
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255 y = seed.choice(list(G.neighbors(x)))
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256 # If the target nodes are the same, skip this pair.
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parents:
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257 if v == y:
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258 continue
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259 if x not in G[u] and y not in G[v]:
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guerler
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260 G.remove_edge(u, v)
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guerler
parents:
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261 G.remove_edge(x, y)
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guerler
parents:
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262 G.add_edge(u, x)
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guerler
parents:
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263 G.add_edge(v, y)
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guerler
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264 swapped.append((u, v, x, y))
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guerler
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265 swapcount += 1
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guerler
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266 n += 1
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guerler
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267 wcount += 1
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guerler
parents:
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268 # If the graph remains connected, increase the window size.
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guerler
parents:
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269 if nx.is_connected(G):
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guerler
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270 window += 1
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guerler
parents:
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271 # Otherwise, undo the changes from the previous window and decrease
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guerler
parents:
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272 # the window size.
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273 else:
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guerler
parents:
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274 while swapped:
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guerler
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275 (u, v, x, y) = swapped.pop()
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guerler
parents:
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276 G.add_edge(u, v)
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guerler
parents:
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277 G.add_edge(x, y)
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guerler
parents:
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278 G.remove_edge(u, x)
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guerler
parents:
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279 G.remove_edge(v, y)
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guerler
parents:
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280 swapcount -= 1
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guerler
parents:
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281 window = int(math.ceil(window / 2))
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guerler
parents:
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282 return swapcount