Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/bridges.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 """Bridge-finding algorithms.""" |
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2 from itertools import chain |
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3 |
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4 import networkx as nx |
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5 from networkx.utils import not_implemented_for |
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6 |
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7 __all__ = ["bridges", "has_bridges", "local_bridges"] |
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8 |
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9 |
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10 @not_implemented_for("multigraph") |
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11 @not_implemented_for("directed") |
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12 def bridges(G, root=None): |
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13 """Generate all bridges in a graph. |
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14 |
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15 A *bridge* in a graph is an edge whose removal causes the number of |
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16 connected components of the graph to increase. Equivalently, a bridge is an |
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17 edge that does not belong to any cycle. |
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18 |
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19 Parameters |
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20 ---------- |
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21 G : undirected graph |
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22 |
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23 root : node (optional) |
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24 A node in the graph `G`. If specified, only the bridges in the |
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25 connected component containing this node will be returned. |
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26 |
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27 Yields |
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28 ------ |
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29 e : edge |
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30 An edge in the graph whose removal disconnects the graph (or |
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31 causes the number of connected components to increase). |
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32 |
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33 Raises |
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34 ------ |
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35 NodeNotFound |
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36 If `root` is not in the graph `G`. |
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37 |
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38 Examples |
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39 -------- |
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40 The barbell graph with parameter zero has a single bridge: |
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41 |
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42 >>> G = nx.barbell_graph(10, 0) |
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43 >>> list(nx.bridges(G)) |
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44 [(9, 10)] |
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45 |
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46 Notes |
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47 ----- |
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48 This is an implementation of the algorithm described in _[1]. An edge is a |
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49 bridge if and only if it is not contained in any chain. Chains are found |
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50 using the :func:`networkx.chain_decomposition` function. |
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51 |
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52 Ignoring polylogarithmic factors, the worst-case time complexity is the |
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53 same as the :func:`networkx.chain_decomposition` function, |
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54 $O(m + n)$, where $n$ is the number of nodes in the graph and $m$ is |
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55 the number of edges. |
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56 |
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57 References |
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58 ---------- |
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59 .. [1] https://en.wikipedia.org/wiki/Bridge_%28graph_theory%29#Bridge-Finding_with_Chain_Decompositions |
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60 """ |
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61 chains = nx.chain_decomposition(G, root=root) |
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62 chain_edges = set(chain.from_iterable(chains)) |
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63 for u, v in G.edges(): |
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64 if (u, v) not in chain_edges and (v, u) not in chain_edges: |
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65 yield u, v |
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66 |
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67 |
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68 @not_implemented_for("multigraph") |
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69 @not_implemented_for("directed") |
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70 def has_bridges(G, root=None): |
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71 """Decide whether a graph has any bridges. |
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72 |
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73 A *bridge* in a graph is an edge whose removal causes the number of |
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74 connected components of the graph to increase. |
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75 |
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76 Parameters |
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77 ---------- |
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78 G : undirected graph |
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79 |
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80 root : node (optional) |
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81 A node in the graph `G`. If specified, only the bridges in the |
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82 connected component containing this node will be considered. |
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83 |
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84 Returns |
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85 ------- |
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86 bool |
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87 Whether the graph (or the connected component containing `root`) |
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88 has any bridges. |
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89 |
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90 Raises |
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91 ------ |
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92 NodeNotFound |
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93 If `root` is not in the graph `G`. |
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94 |
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95 Examples |
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96 -------- |
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97 The barbell graph with parameter zero has a single bridge:: |
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98 |
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99 >>> G = nx.barbell_graph(10, 0) |
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100 >>> nx.has_bridges(G) |
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101 True |
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102 |
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103 On the other hand, the cycle graph has no bridges:: |
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104 |
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105 >>> G = nx.cycle_graph(5) |
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106 >>> nx.has_bridges(G) |
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107 False |
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108 |
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109 Notes |
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110 ----- |
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111 This implementation uses the :func:`networkx.bridges` function, so |
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112 it shares its worst-case time complexity, $O(m + n)$, ignoring |
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113 polylogarithmic factors, where $n$ is the number of nodes in the |
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114 graph and $m$ is the number of edges. |
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115 |
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116 """ |
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117 try: |
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118 next(bridges(G)) |
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119 except StopIteration: |
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120 return False |
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121 else: |
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122 return True |
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123 |
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124 |
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125 @not_implemented_for("multigraph") |
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126 @not_implemented_for("directed") |
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127 def local_bridges(G, with_span=True, weight=None): |
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128 """Iterate over local bridges of `G` optionally computing the span |
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129 |
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130 A *local bridge* is an edge whose endpoints have no common neighbors. |
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131 That is, the edge is not part of a triangle in the graph. |
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132 |
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133 The *span* of a *local bridge* is the shortest path length between |
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134 the endpoints if the local bridge is removed. |
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135 |
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136 Parameters |
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137 ---------- |
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138 G : undirected graph |
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139 |
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140 with_span : bool |
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141 If True, yield a 3-tuple `(u, v, span)` |
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142 |
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143 weight : function, string or None (default: None) |
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144 If function, used to compute edge weights for the span. |
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145 If string, the edge data attribute used in calculating span. |
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146 If None, all edges have weight 1. |
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147 |
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148 Yields |
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149 ------ |
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150 e : edge |
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151 The local bridges as an edge 2-tuple of nodes `(u, v)` or |
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152 as a 3-tuple `(u, v, span)` when `with_span is True`. |
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153 |
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154 Examples |
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155 -------- |
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156 A cycle graph has every edge a local bridge with span N-1. |
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157 |
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158 >>> G = nx.cycle_graph(9) |
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159 >>> (0, 8, 8) in set(nx.local_bridges(G)) |
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160 True |
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161 """ |
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162 if with_span is not True: |
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163 for u, v in G.edges: |
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164 if not (set(G[u]) & set(G[v])): |
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165 yield u, v |
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166 else: |
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167 wt = nx.weighted._weight_function(G, weight) |
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168 for u, v in G.edges: |
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169 if not (set(G[u]) & set(G[v])): |
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170 enodes = {u, v} |
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171 |
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172 def hide_edge(n, nbr, d): |
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173 if n not in enodes or nbr not in enodes: |
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174 return wt(n, nbr, d) |
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175 return None |
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176 |
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177 try: |
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178 span = nx.shortest_path_length(G, u, v, weight=hide_edge) |
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179 yield u, v, span |
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180 except nx.NetworkXNoPath: |
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181 yield u, v, float("inf") |