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annotate planemo/lib/python3.7/site-packages/networkx/algorithms/bridges.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 # bridges.py - bridge-finding algorithms
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3 #
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4 # Copyright 2004-2019 NetworkX developers.
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5 #
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6 # This file is part of NetworkX.
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7 #
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8 # NetworkX is distributed under a BSD license; see LICENSE.txt for more
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9 # information.
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10 """Bridge-finding algorithms."""
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11 from itertools import chain
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12
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13 import networkx as nx
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14 from networkx.utils import not_implemented_for
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15
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16 __all__ = ['bridges', 'has_bridges', 'local_bridges']
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17
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18
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19 @not_implemented_for('multigraph')
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20 @not_implemented_for('directed')
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21 def bridges(G, root=None):
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22 """Generate all bridges in a graph.
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23
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24 A *bridge* in a graph is an edge whose removal causes the number of
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25 connected components of the graph to increase. Equivalently, a bridge is an
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26 edge that does not belong to any cycle.
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27
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28 Parameters
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29 ----------
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30 G : undirected graph
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31
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32 root : node (optional)
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33 A node in the graph `G`. If specified, only the bridges in the
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34 connected component containing this node will be returned.
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35
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36 Yields
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37 ------
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38 e : edge
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39 An edge in the graph whose removal disconnects the graph (or
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40 causes the number of connected components to increase).
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41
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42 Raises
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43 ------
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44 NodeNotFound
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45 If `root` is not in the graph `G`.
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46
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47 Examples
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48 --------
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49 The barbell graph with parameter zero has a single bridge:
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50
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51 >>> G = nx.barbell_graph(10, 0)
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52 >>> list(nx.bridges(G))
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53 [(9, 10)]
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54
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55 Notes
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56 -----
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57 This is an implementation of the algorithm described in _[1]. An edge is a
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58 bridge if and only if it is not contained in any chain. Chains are found
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59 using the :func:`networkx.chain_decomposition` function.
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60
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61 Ignoring polylogarithmic factors, the worst-case time complexity is the
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62 same as the :func:`networkx.chain_decomposition` function,
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63 $O(m + n)$, where $n$ is the number of nodes in the graph and $m$ is
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64 the number of edges.
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65
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66 References
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67 ----------
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68 .. [1] https://en.wikipedia.org/wiki/Bridge_%28graph_theory%29#Bridge-Finding_with_Chain_Decompositions
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69 """
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70 chains = nx.chain_decomposition(G, root=root)
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71 chain_edges = set(chain.from_iterable(chains))
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72 for u, v in G.edges():
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73 if (u, v) not in chain_edges and (v, u) not in chain_edges:
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74 yield u, v
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75
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76
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77 @not_implemented_for('multigraph')
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78 @not_implemented_for('directed')
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79 def has_bridges(G, root=None):
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80 """Decide whether a graph has any bridges.
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81
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82 A *bridge* in a graph is an edge whose removal causes the number of
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83 connected components of the graph to increase.
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84
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85 Parameters
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86 ----------
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87 G : undirected graph
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88
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89 root : node (optional)
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90 A node in the graph `G`. If specified, only the bridges in the
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91 connected component containing this node will be considered.
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92
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93 Returns
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94 -------
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95 bool
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96 Whether the graph (or the connected component containing `root`)
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97 has any bridges.
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98
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99 Raises
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100 ------
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101 NodeNotFound
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102 If `root` is not in the graph `G`.
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103
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104 Examples
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105 --------
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106 The barbell graph with parameter zero has a single bridge::
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107
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108 >>> G = nx.barbell_graph(10, 0)
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109 >>> nx.has_bridges(G)
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110 True
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111
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112 On the other hand, the cycle graph has no bridges::
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113
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114 >>> G = nx.cycle_graph(5)
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115 >>> nx.has_bridges(G)
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116 False
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117
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118 Notes
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119 -----
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120 This implementation uses the :func:`networkx.bridges` function, so
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121 it shares its worst-case time complexity, $O(m + n)$, ignoring
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122 polylogarithmic factors, where $n$ is the number of nodes in the
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123 graph and $m$ is the number of edges.
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124
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125 """
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126 try:
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127 next(bridges(G))
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128 except StopIteration:
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129 return False
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130 else:
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131 return True
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132
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133
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134 @not_implemented_for('multigraph')
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135 @not_implemented_for('directed')
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136 def local_bridges(G, with_span=True, weight=None):
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137 """Iterate over local bridges of `G` optionally computing the span
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138
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139 A *local bridge* is an edge whose endpoints have no common neighbors.
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140 That is, the edge is not part of a triangle in the graph.
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141
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142 The *span* of a *local bridge* is the shortest path length between
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143 the endpoints if the local bridge is removed.
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144
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145 Parameters
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146 ----------
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147 G : undirected graph
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148
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149 with_span : bool
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150 If True, yield a 3-tuple `(u, v, span)`
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151
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152 weight : function, string or None (default: None)
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153 If function, used to compute edge weights for the span.
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154 If string, the edge data attribute used in calculating span.
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155 If None, all edges have weight 1.
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156
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157 Yields
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158 ------
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159 e : edge
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160 The local bridges as an edge 2-tuple of nodes `(u, v)` or
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161 as a 3-tuple `(u, v, span)` when `with_span is True`.
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162
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163 Examples
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164 --------
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165 A cycle graph has every edge a local bridge with span N-1.
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166
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167 >>> G = nx.cycle_graph(9)
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168 >>> (0, 8, 8) in set(nx.local_bridges(G))
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169 True
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170 """
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171 if with_span is not True:
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172 for u, v in G.edges:
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173 if not (set(G[u]) & set(G[v])):
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174 yield u, v
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175 else:
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176 wt = nx.weighted._weight_function(G, weight)
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177 for u, v in G.edges:
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178 if not (set(G[u]) & set(G[v])):
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179 enodes = {u, v}
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180
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181 def hide_edge(n, nbr, d):
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182 if n not in enodes or nbr not in enodes:
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183 return wt(n, nbr, d)
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184 return None
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185
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186 try:
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187 span = nx.shortest_path_length(G, u, v, weight=hide_edge)
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188 yield u, v, span
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189 except nx.NetworkXNoPath:
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190 yield u, v, float('inf')