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annotate env/lib/python3.7/site-packages/networkx/linalg/graphmatrix.py @ 2:6af9afd405e9 draft

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"planemo upload commit 0a63dd5f4d38a1f6944587f52a8cd79874177fc1"
author shellac
date Thu, 14 May 2020 14:56:58 -0400
parents 26e78fe6e8c4
children
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1 """
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2 Adjacency matrix and incidence matrix of graphs.
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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 import networkx as nx
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11 __author__ = "\n".join(['Aric Hagberg (hagberg@lanl.gov)',
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12 'Pieter Swart (swart@lanl.gov)',
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13 'Dan Schult(dschult@colgate.edu)'])
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14
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15 __all__ = ['incidence_matrix',
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16 'adj_matrix', 'adjacency_matrix',
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17 ]
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18
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19
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20 def incidence_matrix(G, nodelist=None, edgelist=None,
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21 oriented=False, weight=None):
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22 """Returns incidence matrix of G.
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23
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24 The incidence matrix assigns each row to a node and each column to an edge.
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25 For a standard incidence matrix a 1 appears wherever a row's node is
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26 incident on the column's edge. For an oriented incidence matrix each
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27 edge is assigned an orientation (arbitrarily for undirected and aligning to
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28 direction for directed). A -1 appears for the tail of an edge and 1
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29 for the head of the edge. The elements are zero otherwise.
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30
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31 Parameters
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32 ----------
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33 G : graph
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34 A NetworkX graph
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35
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36 nodelist : list, optional (default= all nodes in G)
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37 The rows are ordered according to the nodes in nodelist.
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38 If nodelist is None, then the ordering is produced by G.nodes().
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39
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40 edgelist : list, optional (default= all edges in G)
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41 The columns are ordered according to the edges in edgelist.
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42 If edgelist is None, then the ordering is produced by G.edges().
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43
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44 oriented: bool, optional (default=False)
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45 If True, matrix elements are +1 or -1 for the head or tail node
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46 respectively of each edge. If False, +1 occurs at both nodes.
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47
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48 weight : string or None, optional (default=None)
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49 The edge data key used to provide each value in the matrix.
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50 If None, then each edge has weight 1. Edge weights, if used,
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51 should be positive so that the orientation can provide the sign.
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52
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53 Returns
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54 -------
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55 A : SciPy sparse matrix
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56 The incidence matrix of G.
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57
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58 Notes
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59 -----
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60 For MultiGraph/MultiDiGraph, the edges in edgelist should be
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61 (u,v,key) 3-tuples.
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62
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63 "Networks are the best discrete model for so many problems in
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64 applied mathematics" [1]_.
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65
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66 References
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67 ----------
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68 .. [1] Gil Strang, Network applications: A = incidence matrix,
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69 http://academicearth.org/lectures/network-applications-incidence-matrix
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70 """
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71 import scipy.sparse
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72 if nodelist is None:
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73 nodelist = list(G)
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74 if edgelist is None:
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75 if G.is_multigraph():
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76 edgelist = list(G.edges(keys=True))
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77 else:
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78 edgelist = list(G.edges())
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79 A = scipy.sparse.lil_matrix((len(nodelist), len(edgelist)))
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80 node_index = dict((node, i) for i, node in enumerate(nodelist))
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81 for ei, e in enumerate(edgelist):
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82 (u, v) = e[:2]
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83 if u == v:
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84 continue # self loops give zero column
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85 try:
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86 ui = node_index[u]
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87 vi = node_index[v]
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88 except KeyError:
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89 raise nx.NetworkXError('node %s or %s in edgelist '
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90 'but not in nodelist' % (u, v))
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91 if weight is None:
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92 wt = 1
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93 else:
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94 if G.is_multigraph():
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95 ekey = e[2]
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96 wt = G[u][v][ekey].get(weight, 1)
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97 else:
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98 wt = G[u][v].get(weight, 1)
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99 if oriented:
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100 A[ui, ei] = -wt
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101 A[vi, ei] = wt
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102 else:
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103 A[ui, ei] = wt
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104 A[vi, ei] = wt
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105 return A.asformat('csc')
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106
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107
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108 def adjacency_matrix(G, nodelist=None, weight='weight'):
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109 """Returns adjacency matrix of G.
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110
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111 Parameters
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112 ----------
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113 G : graph
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114 A NetworkX graph
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115
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116 nodelist : list, optional
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117 The rows and columns are ordered according to the nodes in nodelist.
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118 If nodelist is None, then the ordering is produced by G.nodes().
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119
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120 weight : string or None, optional (default='weight')
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121 The edge data key used to provide each value in the matrix.
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122 If None, then each edge has weight 1.
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123
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124 Returns
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125 -------
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126 A : SciPy sparse matrix
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127 Adjacency matrix representation of G.
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128
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129 Notes
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130 -----
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131 For directed graphs, entry i,j corresponds to an edge from i to j.
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132
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133 If you want a pure Python adjacency matrix representation try
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134 networkx.convert.to_dict_of_dicts which will return a
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135 dictionary-of-dictionaries format that can be addressed as a
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136 sparse matrix.
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137
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138 For MultiGraph/MultiDiGraph with parallel edges the weights are summed.
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139 See to_numpy_matrix for other options.
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140
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141 The convention used for self-loop edges in graphs is to assign the
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142 diagonal matrix entry value to the edge weight attribute
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143 (or the number 1 if the edge has no weight attribute). If the
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144 alternate convention of doubling the edge weight is desired the
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145 resulting Scipy sparse matrix can be modified as follows:
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146
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147 >>> import scipy as sp
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148 >>> G = nx.Graph([(1,1)])
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149 >>> A = nx.adjacency_matrix(G)
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150 >>> print(A.todense())
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151 [[1]]
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152 >>> A.setdiag(A.diagonal()*2)
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153 >>> print(A.todense())
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154 [[2]]
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155
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156 See Also
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157 --------
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158 to_numpy_matrix
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159 to_scipy_sparse_matrix
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160 to_dict_of_dicts
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161 adjacency_spectrum
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162 """
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163 return nx.to_scipy_sparse_matrix(G, nodelist=nodelist, weight=weight)
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164
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165
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166 adj_matrix = adjacency_matrix
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167
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168
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169 # fixture for pytest
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170 def setup_module(module):
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171 import pytest
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172 scipy = pytest.importorskip('scipy')