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annotate planemo/lib/python3.7/site-packages/networkx/algorithms/hybrid.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 # Copyright (C) 2004-2019 by
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3 # Aric Hagberg <hagberg@lanl.gov>
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4 # Dan Schult <dschult@colgate.edu>
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5 # Pieter Swart <swart@lanl.gov>
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6 # All rights reserved.
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7 # BSD license.
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8 #
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9 # Authors: Aric Hagberg (hagberg@lanl.gov) and Dan Schult (dschult@colgate.edu)
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10 #
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11 """
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12 Provides functions for finding and testing for locally `(k, l)`-connected
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13 graphs.
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14
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15 """
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16 import copy
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17 import networkx as nx
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18
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19 __all__ = ['kl_connected_subgraph', 'is_kl_connected']
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20
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21
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22 def kl_connected_subgraph(G, k, l, low_memory=False, same_as_graph=False):
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23 """Returns the maximum locally `(k, l)`-connected subgraph of `G`.
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24
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25 A graph is locally `(k, l)`-connected if for each edge `(u, v)` in the
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26 graph there are at least `l` edge-disjoint paths of length at most `k`
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27 joining `u` to `v`.
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28
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29 Parameters
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30 ----------
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31 G : NetworkX graph
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32 The graph in which to find a maximum locally `(k, l)`-connected
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33 subgraph.
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34
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35 k : integer
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36 The maximum length of paths to consider. A higher number means a looser
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37 connectivity requirement.
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38
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39 l : integer
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40 The number of edge-disjoint paths. A higher number means a stricter
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41 connectivity requirement.
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42
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43 low_memory : bool
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44 If this is True, this function uses an algorithm that uses slightly
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45 more time but less memory.
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46
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47 same_as_graph : bool
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48 If True then return a tuple of the form `(H, is_same)`,
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49 where `H` is the maximum locally `(k, l)`-connected subgraph and
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50 `is_same` is a Boolean representing whether `G` is locally `(k,
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51 l)`-connected (and hence, whether `H` is simply a copy of the input
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52 graph `G`).
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53
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54 Returns
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55 -------
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56 NetworkX graph or two-tuple
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57 If `same_as_graph` is True, then this function returns a
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58 two-tuple as described above. Otherwise, it returns only the maximum
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59 locally `(k, l)`-connected subgraph.
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60
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61 See also
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62 --------
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63 is_kl_connected
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64
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65 References
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66 ----------
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67 .. [1]: Chung, Fan and Linyuan Lu. "The Small World Phenomenon in Hybrid
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68 Power Law Graphs." *Complex Networks*. Springer Berlin Heidelberg,
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69 2004. 89--104.
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70
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71 """
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72 H = copy.deepcopy(G) # subgraph we construct by removing from G
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73
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74 graphOK = True
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75 deleted_some = True # hack to start off the while loop
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76 while deleted_some:
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77 deleted_some = False
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78 # We use `for edge in list(H.edges()):` instead of
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79 # `for edge in H.edges():` because we edit the graph `H` in
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80 # the loop. Hence using an iterator will result in
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81 # `RuntimeError: dictionary changed size during iteration`
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82 for edge in list(H.edges()):
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83 (u, v) = edge
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84 # Get copy of graph needed for this search
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85 if low_memory:
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86 verts = set([u, v])
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87 for i in range(k):
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88 for w in verts.copy():
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89 verts.update(G[w])
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90 G2 = G.subgraph(verts).copy()
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91 else:
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92 G2 = copy.deepcopy(G)
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93 ###
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94 path = [u, v]
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95 cnt = 0
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96 accept = 0
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97 while path:
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98 cnt += 1 # Found a path
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99 if cnt >= l:
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100 accept = 1
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101 break
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102 # record edges along this graph
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103 prev = u
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104 for w in path:
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105 if prev != w:
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106 G2.remove_edge(prev, w)
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107 prev = w
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108 # path = shortest_path(G2, u, v, k) # ??? should "Cutoff" be k+1?
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109 try:
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110 path = nx.shortest_path(G2, u, v) # ??? should "Cutoff" be k+1?
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111 except nx.NetworkXNoPath:
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112 path = False
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113 # No Other Paths
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114 if accept == 0:
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115 H.remove_edge(u, v)
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116 deleted_some = True
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117 if graphOK:
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118 graphOK = False
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119 # We looked through all edges and removed none of them.
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120 # So, H is the maximal (k,l)-connected subgraph of G
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121 if same_as_graph:
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122 return (H, graphOK)
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123 return H
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124
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125
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126 def is_kl_connected(G, k, l, low_memory=False):
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127 """Returns True if and only if `G` is locally `(k, l)`-connected.
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128
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129 A graph is locally `(k, l)`-connected if for each edge `(u, v)` in the
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130 graph there are at least `l` edge-disjoint paths of length at most `k`
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131 joining `u` to `v`.
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132
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133 Parameters
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134 ----------
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135 G : NetworkX graph
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136 The graph to test for local `(k, l)`-connectedness.
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137
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138 k : integer
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139 The maximum length of paths to consider. A higher number means a looser
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140 connectivity requirement.
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141
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142 l : integer
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143 The number of edge-disjoint paths. A higher number means a stricter
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144 connectivity requirement.
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145
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146 low_memory : bool
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147 If this is True, this function uses an algorithm that uses slightly
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148 more time but less memory.
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149
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150 Returns
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151 -------
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152 bool
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153 Whether the graph is locally `(k, l)`-connected subgraph.
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154
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155 See also
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156 --------
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157 kl_connected_subgraph
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158
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159 References
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160 ----------
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161 .. [1]: Chung, Fan and Linyuan Lu. "The Small World Phenomenon in Hybrid
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162 Power Law Graphs." *Complex Networks*. Springer Berlin Heidelberg,
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163 2004. 89--104.
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164
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165 """
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166 graphOK = True
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167 for edge in G.edges():
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168 (u, v) = edge
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169 # Get copy of graph needed for this search
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170 if low_memory:
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171 verts = set([u, v])
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172 for i in range(k):
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173 [verts.update(G.neighbors(w)) for w in verts.copy()]
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174 G2 = G.subgraph(verts)
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175 else:
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176 G2 = copy.deepcopy(G)
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177 ###
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178 path = [u, v]
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179 cnt = 0
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180 accept = 0
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181 while path:
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182 cnt += 1 # Found a path
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183 if cnt >= l:
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184 accept = 1
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185 break
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186 # record edges along this graph
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187 prev = u
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188 for w in path:
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189 if w != prev:
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190 G2.remove_edge(prev, w)
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191 prev = w
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192 # path = shortest_path(G2, u, v, k) # ??? should "Cutoff" be k+1?
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193 try:
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194 path = nx.shortest_path(G2, u, v) # ??? should "Cutoff" be k+1?
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195 except nx.NetworkXNoPath:
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196 path = False
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197 # No Other Paths
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198 if accept == 0:
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199 graphOK = False
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200 break
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201 # return status
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202 return graphOK