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

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"planemo upload commit 0a63dd5f4d38a1f6944587f52a8cd79874177fc1"
author shellac
date Thu, 14 May 2020 14:56:58 -0400 (2020-05-14)
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1 """Modularity matrix of graphs.
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2 """
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3 # Copyright (C) 2004-2019 by
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4 # Aric Hagberg <hagberg@lanl.gov>
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5 # Dan Schult <dschult@colgate.edu>
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6 # Pieter Swart <swart@lanl.gov>
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7 # All rights reserved.
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8 # BSD license.
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9 import networkx as nx
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10 from networkx.utils import not_implemented_for
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11 __author__ = "\n".join(['Aric Hagberg <aric.hagberg@gmail.com>',
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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 'Jean-Gabriel Young (Jean.gabriel.young@gmail.com)'])
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15 __all__ = ['modularity_matrix', 'directed_modularity_matrix']
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16
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17
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18 @not_implemented_for('directed')
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19 @not_implemented_for('multigraph')
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20 def modularity_matrix(G, nodelist=None, weight=None):
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21 r"""Returns the modularity matrix of G.
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22
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23 The modularity matrix is the matrix B = A - <A>, where A is the adjacency
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24 matrix and <A> is the average adjacency matrix, assuming that the graph
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25 is described by the configuration model.
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26
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27 More specifically, the element B_ij of B is defined as
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28
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29 .. math::
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30 A_{ij} - {k_i k_j \over 2 m}
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31
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32 where k_i is the degree of node i, and where m is the number of edges
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33 in the graph. When weight is set to a name of an attribute edge, Aij, k_i,
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34 k_j and m are computed using its value.
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35
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36 Parameters
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37 ----------
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38 G : Graph
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39 A NetworkX graph
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40
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41 nodelist : list, optional
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42 The rows and columns are ordered according to the nodes in nodelist.
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43 If nodelist is None, then the ordering is produced by G.nodes().
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44
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45 weight : string or None, optional (default=None)
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46 The edge attribute that holds the numerical value used for
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47 the edge weight. If None then all edge weights are 1.
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48
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49 Returns
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50 -------
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51 B : Numpy matrix
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52 The modularity matrix of G.
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53
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54 Examples
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55 --------
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56 >>> import networkx as nx
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57 >>> k =[3, 2, 2, 1, 0]
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58 >>> G = nx.havel_hakimi_graph(k)
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59 >>> B = nx.modularity_matrix(G)
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60
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61
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62 See Also
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63 --------
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64 to_numpy_matrix
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65 modularity_spectrum
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66 adjacency_matrix
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67 directed_modularity_matrix
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68
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69 References
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70 ----------
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71 .. [1] M. E. J. Newman, "Modularity and community structure in networks",
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72 Proc. Natl. Acad. Sci. USA, vol. 103, pp. 8577-8582, 2006.
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73 """
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74 if nodelist is None:
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75 nodelist = list(G)
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76 A = nx.to_scipy_sparse_matrix(G, nodelist=nodelist, weight=weight,
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77 format='csr')
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78 k = A.sum(axis=1)
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79 m = k.sum() * 0.5
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80 # Expected adjacency matrix
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81 X = k * k.transpose() / (2 * m)
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82 return A - X
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83
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84
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85 @not_implemented_for('undirected')
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86 @not_implemented_for('multigraph')
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87 def directed_modularity_matrix(G, nodelist=None, weight=None):
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88 """Returns the directed modularity matrix of G.
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89
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90 The modularity matrix is the matrix B = A - <A>, where A is the adjacency
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91 matrix and <A> is the expected adjacency matrix, assuming that the graph
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92 is described by the configuration model.
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93
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94 More specifically, the element B_ij of B is defined as
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95
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96 .. math::
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97 B_{ij} = A_{ij} - k_i^{out} k_j^{in} / m
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98
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99 where :math:`k_i^{in}` is the in degree of node i, and :math:`k_j^{out}` is the out degree
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100 of node j, with m the number of edges in the graph. When weight is set
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101 to a name of an attribute edge, Aij, k_i, k_j and m are computed using
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102 its value.
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103
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104 Parameters
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105 ----------
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106 G : DiGraph
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107 A NetworkX DiGraph
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108
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109 nodelist : list, optional
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110 The rows and columns are ordered according to the nodes in nodelist.
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111 If nodelist is None, then the ordering is produced by G.nodes().
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112
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113 weight : string or None, optional (default=None)
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114 The edge attribute that holds the numerical value used for
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115 the edge weight. If None then all edge weights are 1.
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116
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117 Returns
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118 -------
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119 B : Numpy matrix
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120 The modularity matrix of G.
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121
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122 Examples
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123 --------
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124 >>> import networkx as nx
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125 >>> G = nx.DiGraph()
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126 >>> G.add_edges_from(((1,2), (1,3), (3,1), (3,2), (3,5), (4,5), (4,6),
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127 ... (5,4), (5,6), (6,4)))
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128 >>> B = nx.directed_modularity_matrix(G)
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129
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130
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131 Notes
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132 -----
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133 NetworkX defines the element A_ij of the adjacency matrix as 1 if there
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134 is a link going from node i to node j. Leicht and Newman use the opposite
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135 definition. This explains the different expression for B_ij.
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136
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137 See Also
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138 --------
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139 to_numpy_matrix
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140 modularity_spectrum
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141 adjacency_matrix
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142 modularity_matrix
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143
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144 References
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145 ----------
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146 .. [1] E. A. Leicht, M. E. J. Newman,
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147 "Community structure in directed networks",
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148 Phys. Rev Lett., vol. 100, no. 11, p. 118703, 2008.
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149 """
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150 if nodelist is None:
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151 nodelist = list(G)
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152 A = nx.to_scipy_sparse_matrix(G, nodelist=nodelist, weight=weight,
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153 format='csr')
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154 k_in = A.sum(axis=0)
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155 k_out = A.sum(axis=1)
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156 m = k_in.sum()
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157 # Expected adjacency matrix
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158 X = k_out * k_in / m
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159 return A - X
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160
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161
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162 # fixture for pytest
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163 def setup_module(module):
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164 import pytest
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165 numpy = pytest.importorskip('numpy')
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166 scipy = pytest.importorskip('scipy')