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annotate planemo/lib/python3.7/site-packages/networkx/algorithms/chains.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 # chains.py - functions for finding chains in a graph
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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 """Functions for finding chains in a graph."""
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11
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12 import networkx as nx
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13 from networkx.utils import not_implemented_for
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14
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15
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16 @not_implemented_for('directed')
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17 @not_implemented_for('multigraph')
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18 def chain_decomposition(G, root=None):
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19 """Returns the chain decomposition of a graph.
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20
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21 The *chain decomposition* of a graph with respect a depth-first
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22 search tree is a set of cycles or paths derived from the set of
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23 fundamental cycles of the tree in the following manner. Consider
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24 each fundamental cycle with respect to the given tree, represented
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25 as a list of edges beginning with the nontree edge oriented away
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26 from the root of the tree. For each fundamental cycle, if it
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27 overlaps with any previous fundamental cycle, just take the initial
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28 non-overlapping segment, which is a path instead of a cycle. Each
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29 cycle or path is called a *chain*. For more information, see [1]_.
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30
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31 Parameters
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32 ----------
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33 G : undirected graph
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34
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35 root : node (optional)
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36 A node in the graph `G`. If specified, only the chain
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37 decomposition for the connected component containing this node
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38 will be returned. This node indicates the root of the depth-first
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39 search tree.
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40
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41 Yields
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42 ------
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43 chain : list
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44 A list of edges representing a chain. There is no guarantee on
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45 the orientation of the edges in each chain (for example, if a
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46 chain includes the edge joining nodes 1 and 2, the chain may
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47 include either (1, 2) or (2, 1)).
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48
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49 Raises
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50 ------
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51 NodeNotFound
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52 If `root` is not in the graph `G`.
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53
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54 Notes
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55 -----
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56 The worst-case running time of this implementation is linear in the
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57 number of nodes and number of edges [1]_.
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58
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59 References
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60 ----------
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61 .. [1] Jens M. Schmidt (2013). "A simple test on 2-vertex-
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62 and 2-edge-connectivity." *Information Processing Letters*,
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63 113, 241–244. Elsevier. <https://doi.org/10.1016/j.ipl.2013.01.016>
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64
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65 """
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66
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67 def _dfs_cycle_forest(G, root=None):
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68 """Builds a directed graph composed of cycles from the given graph.
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69
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70 `G` is an undirected simple graph. `root` is a node in the graph
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71 from which the depth-first search is started.
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72
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73 This function returns both the depth-first search cycle graph
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74 (as a :class:`~networkx.DiGraph`) and the list of nodes in
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75 depth-first preorder. The depth-first search cycle graph is a
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76 directed graph whose edges are the edges of `G` oriented toward
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77 the root if the edge is a tree edge and away from the root if
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78 the edge is a non-tree edge. If `root` is not specified, this
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79 performs a depth-first search on each connected component of `G`
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80 and returns a directed forest instead.
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81
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82 If `root` is not in the graph, this raises :exc:`KeyError`.
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83
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84 """
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85 # Create a directed graph from the depth-first search tree with
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86 # root node `root` in which tree edges are directed toward the
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87 # root and nontree edges are directed away from the root. For
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88 # each node with an incident nontree edge, this creates a
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89 # directed cycle starting with the nontree edge and returning to
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90 # that node.
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91 #
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92 # The `parent` node attribute stores the parent of each node in
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93 # the DFS tree. The `nontree` edge attribute indicates whether
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94 # the edge is a tree edge or a nontree edge.
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95 #
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96 # We also store the order of the nodes found in the depth-first
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97 # search in the `nodes` list.
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98 H = nx.DiGraph()
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99 nodes = []
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100 for u, v, d in nx.dfs_labeled_edges(G, source=root):
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101 if d == 'forward':
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102 # `dfs_labeled_edges()` yields (root, root, 'forward')
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103 # if it is beginning the search on a new connected
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104 # component.
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105 if u == v:
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106 H.add_node(v, parent=None)
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107 nodes.append(v)
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108 else:
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109 H.add_node(v, parent=u)
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110 H.add_edge(v, u, nontree=False)
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111 nodes.append(v)
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112 # `dfs_labeled_edges` considers nontree edges in both
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113 # orientations, so we need to not add the edge if it its
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114 # other orientation has been added.
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115 elif d == 'nontree' and v not in H[u]:
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116 H.add_edge(v, u, nontree=True)
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117 else:
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118 # Do nothing on 'reverse' edges; we only care about
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119 # forward and nontree edges.
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120 pass
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121 return H, nodes
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122
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123 def _build_chain(G, u, v, visited):
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124 """Generate the chain starting from the given nontree edge.
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125
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126 `G` is a DFS cycle graph as constructed by
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127 :func:`_dfs_cycle_graph`. The edge (`u`, `v`) is a nontree edge
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128 that begins a chain. `visited` is a set representing the nodes
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129 in `G` that have already been visited.
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130
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131 This function yields the edges in an initial segment of the
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132 fundamental cycle of `G` starting with the nontree edge (`u`,
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133 `v`) that includes all the edges up until the first node that
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134 appears in `visited`. The tree edges are given by the 'parent'
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135 node attribute. The `visited` set is updated to add each node in
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136 an edge yielded by this function.
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137
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138 """
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139 while v not in visited:
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140 yield u, v
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141 visited.add(v)
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142 u, v = v, G.nodes[v]['parent']
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143 yield u, v
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144
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145 # Create a directed version of H that has the DFS edges directed
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146 # toward the root and the nontree edges directed away from the root
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147 # (in each connected component).
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148 H, nodes = _dfs_cycle_forest(G, root)
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149
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150 # Visit the nodes again in DFS order. For each node, and for each
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151 # nontree edge leaving that node, compute the fundamental cycle for
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152 # that nontree edge starting with that edge. If the fundamental
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153 # cycle overlaps with any visited nodes, just take the prefix of the
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154 # cycle up to the point of visited nodes.
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155 #
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156 # We repeat this process for each connected component (implicitly,
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157 # since `nodes` already has a list of the nodes grouped by connected
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158 # component).
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159 visited = set()
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160 for u in nodes:
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161 visited.add(u)
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162 # For each nontree edge going out of node u...
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163 edges = ((u, v) for u, v, d in H.out_edges(u, data='nontree') if d)
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164 for u, v in edges:
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165 # Create the cycle or cycle prefix starting with the
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166 # nontree edge.
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167 chain = list(_build_chain(H, u, v, visited))
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168 yield chain