Mercurial > repos > shellac > guppy_basecaller

annotate env/lib/python3.7/site-packages/networkx/convert_matrix.py @ 4:79f47841a781 draft

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"planemo upload commit 2a0fe2cc28b09e101d37293e53e82f61762262ec"
author shellac
date Thu, 14 May 2020 16:47:39 -0400
parents 26e78fe6e8c4
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1 # Copyright (C) 2006-2019 by
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2 # Aric Hagberg <hagberg@lanl.gov>
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3 # Dan Schult <dschult@colgate.edu>
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4 # Pieter Swart <swart@lanl.gov>
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5 # All rights reserved.
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6 # BSD license.
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7 """Functions to convert NetworkX graphs to and from numpy/scipy matrices.
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8
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9 The preferred way of converting data to a NetworkX graph is through the
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10 graph constructor. The constructor calls the to_networkx_graph() function
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11 which attempts to guess the input type and convert it automatically.
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12
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13 Examples
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14 --------
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15 Create a 10 node random graph from a numpy matrix
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16
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17 >>> import numpy as np
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18 >>> a = np.random.randint(0, 2, size=(10, 10))
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19 >>> D = nx.DiGraph(a)
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20
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21 or equivalently
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22
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23 >>> D = nx.to_networkx_graph(a, create_using=nx.DiGraph)
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24
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25 See Also
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26 --------
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27 nx_agraph, nx_pydot
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28 """
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29
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30 import itertools
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31 import networkx as nx
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32 from networkx.utils import not_implemented_for
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33
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34 __all__ = ['from_numpy_matrix', 'to_numpy_matrix',
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35 'from_pandas_adjacency', 'to_pandas_adjacency',
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36 'from_pandas_edgelist', 'to_pandas_edgelist',
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37 'to_numpy_recarray',
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38 'from_scipy_sparse_matrix', 'to_scipy_sparse_matrix',
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39 'from_numpy_array', 'to_numpy_array']
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40
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41
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42 def to_pandas_adjacency(G, nodelist=None, dtype=None, order=None,
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43 multigraph_weight=sum, weight='weight', nonedge=0.0):
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44 """Returns the graph adjacency matrix as a Pandas DataFrame.
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45
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46 Parameters
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47 ----------
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48 G : graph
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49 The NetworkX graph used to construct the Pandas DataFrame.
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50
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51 nodelist : list, optional
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52 The rows and columns are ordered according to the nodes in `nodelist`.
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53 If `nodelist` is None, then the ordering is produced by G.nodes().
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54
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55 multigraph_weight : {sum, min, max}, optional
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56 An operator that determines how weights in multigraphs are handled.
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57 The default is to sum the weights of the multiple edges.
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58
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59 weight : string or None, optional
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60 The edge attribute that holds the numerical value used for
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61 the edge weight. If an edge does not have that attribute, then the
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62 value 1 is used instead.
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63
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64 nonedge : float, optional
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65 The matrix values corresponding to nonedges are typically set to zero.
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66 However, this could be undesirable if there are matrix values
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67 corresponding to actual edges that also have the value zero. If so,
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68 one might prefer nonedges to have some other value, such as nan.
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69
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70 Returns
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71 -------
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72 df : Pandas DataFrame
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73 Graph adjacency matrix
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74
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75 Notes
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76 -----
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77 For directed graphs, entry i,j corresponds to an edge from i to j.
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78
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79 The DataFrame entries are assigned to the weight edge attribute. When
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80 an edge does not have a weight attribute, the value of the entry is set to
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81 the number 1. For multiple (parallel) edges, the values of the entries
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82 are determined by the 'multigraph_weight' parameter. The default is to
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83 sum the weight attributes for each of the parallel edges.
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84
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85 When `nodelist` does not contain every node in `G`, the matrix is built
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86 from the subgraph of `G` that is induced by the nodes in `nodelist`.
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87
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88 The convention used for self-loop edges in graphs is to assign the
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89 diagonal matrix entry value to the weight attribute of the edge
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90 (or the number 1 if the edge has no weight attribute). If the
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91 alternate convention of doubling the edge weight is desired the
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92 resulting Pandas DataFrame can be modified as follows:
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93
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94 >>> import pandas as pd
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95 >>> pd.options.display.max_columns = 20
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96 >>> import numpy as np
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97 >>> G = nx.Graph([(1, 1)])
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98 >>> df = nx.to_pandas_adjacency(G, dtype=int)
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99 >>> df
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100 1
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101 1 1
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102 >>> df.values[np.diag_indices_from(df)] *= 2
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103 >>> df
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104 1
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105 1 2
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106
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107 Examples
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108 --------
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109 >>> G = nx.MultiDiGraph()
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110 >>> G.add_edge(0, 1, weight=2)
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111 0
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112 >>> G.add_edge(1, 0)
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113 0
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114 >>> G.add_edge(2, 2, weight=3)
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115 0
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116 >>> G.add_edge(2, 2)
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117 1
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118 >>> nx.to_pandas_adjacency(G, nodelist=[0, 1, 2], dtype=int)
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119 0 1 2
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120 0 0 2 0
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121 1 1 0 0
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122 2 0 0 4
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123
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124 """
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125 import pandas as pd
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126 M = to_numpy_array(G, nodelist=nodelist, dtype=dtype, order=order,
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127 multigraph_weight=multigraph_weight, weight=weight,
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128 nonedge=nonedge)
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129 if nodelist is None:
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130 nodelist = list(G)
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131 return pd.DataFrame(data=M, index=nodelist, columns=nodelist)
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132
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133
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134 def from_pandas_adjacency(df, create_using=None):
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135 r"""Returns a graph from Pandas DataFrame.
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136
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137 The Pandas DataFrame is interpreted as an adjacency matrix for the graph.
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138
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139 Parameters
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140 ----------
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141 df : Pandas DataFrame
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142 An adjacency matrix representation of a graph
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143
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144 create_using : NetworkX graph constructor, optional (default=nx.Graph)
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145 Graph type to create. If graph instance, then cleared before populated.
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146
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147 Notes
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148 -----
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149 For directed graphs, explicitly mention create_using=nx.Digraph,
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150 and entry i,j of df corresponds to an edge from i to j.
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151
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152 If the numpy matrix has a single data type for each matrix entry it
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153 will be converted to an appropriate Python data type.
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154
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155 If the numpy matrix has a user-specified compound data type the names
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156 of the data fields will be used as attribute keys in the resulting
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157 NetworkX graph.
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158
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159 See Also
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160 --------
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161 to_pandas_adjacency
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162
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163 Examples
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164 --------
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165 Simple integer weights on edges:
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166
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167 >>> import pandas as pd
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168 >>> pd.options.display.max_columns = 20
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169 >>> df = pd.DataFrame([[1, 1], [2, 1]])
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170 >>> df
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171 0 1
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172 0 1 1
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173 1 2 1
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174 >>> G = nx.from_pandas_adjacency(df)
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175 >>> G.name = 'Graph from pandas adjacency matrix'
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176 >>> print(nx.info(G))
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177 Name: Graph from pandas adjacency matrix
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178 Type: Graph
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179 Number of nodes: 2
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180 Number of edges: 3
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181 Average degree: 3.0000
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182
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183 """
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184
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185 try:
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186 df = df[df.index]
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187 except Exception:
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188 msg = "%s not in columns"
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189 missing = list(set(df.index).difference(set(df.columns)))
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190 raise nx.NetworkXError("Columns must match Indices.", msg % missing)
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191
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192 A = df.values
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193 G = from_numpy_matrix(A, create_using=create_using)
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194
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195 nx.relabel.relabel_nodes(G, dict(enumerate(df.columns)), copy=False)
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196 return G
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197
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198
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199 def to_pandas_edgelist(G, source='source', target='target', nodelist=None,
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200 dtype=None, order=None):
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201 """Returns the graph edge list as a Pandas DataFrame.
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202
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203 Parameters
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204 ----------
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205 G : graph
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206 The NetworkX graph used to construct the Pandas DataFrame.
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207
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208 source : str or int, optional
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209 A valid column name (string or integer) for the source nodes (for the
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210 directed case).
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211
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212 target : str or int, optional
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213 A valid column name (string or integer) for the target nodes (for the
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214 directed case).
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215
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216 nodelist : list, optional
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217 Use only nodes specified in nodelist
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218
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219 Returns
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220 -------
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221 df : Pandas DataFrame
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222 Graph edge list
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223
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224 Examples
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225 --------
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226 >>> G = nx.Graph([('A', 'B', {'cost': 1, 'weight': 7}),
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227 ... ('C', 'E', {'cost': 9, 'weight': 10})])
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228 >>> df = nx.to_pandas_edgelist(G, nodelist=['A', 'C'])
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229 >>> df[['source', 'target', 'cost', 'weight']]
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230 source target cost weight
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231 0 A B 1 7
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232 1 C E 9 10
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233
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234 """
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235 import pandas as pd
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236 if nodelist is None:
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237 edgelist = G.edges(data=True)
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238 else:
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239 edgelist = G.edges(nodelist, data=True)
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240 source_nodes = [s for s, t, d in edgelist]
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241 target_nodes = [t for s, t, d in edgelist]
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242 all_keys = set().union(*(d.keys() for s, t, d in edgelist))
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243 edge_attr = {k: [d.get(k, float("nan")) for s, t, d in edgelist]
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244 for k in all_keys}
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245 edgelistdict = {source: source_nodes, target: target_nodes}
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246 edgelistdict.update(edge_attr)
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247 return pd.DataFrame(edgelistdict)
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248
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249
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250 def from_pandas_edgelist(df, source='source', target='target', edge_attr=None,
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251 create_using=None):
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252 """Returns a graph from Pandas DataFrame containing an edge list.
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253
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254 The Pandas DataFrame should contain at least two columns of node names and
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255 zero or more columns of edge attributes. Each row will be processed as one
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256 edge instance.
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257
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258 Note: This function iterates over DataFrame.values, which is not
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259 guaranteed to retain the data type across columns in the row. This is only
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260 a problem if your row is entirely numeric and a mix of ints and floats. In
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261 that case, all values will be returned as floats. See the
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262 DataFrame.iterrows documentation for an example.
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263
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264 Parameters
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265 ----------
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266 df : Pandas DataFrame
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267 An edge list representation of a graph
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268
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269 source : str or int
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270 A valid column name (string or integer) for the source nodes (for the
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271 directed case).
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272
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273 target : str or int
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274 A valid column name (string or integer) for the target nodes (for the
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275 directed case).
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276
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277 edge_attr : str or int, iterable, True, or None
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278 A valid column name (str or int) or iterable of column names that are
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279 used to retrieve items and add them to the graph as edge attributes.
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280 If `True`, all of the remaining columns will be added.
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281 If `None`, no edge attributes are added to the graph.
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282
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283 create_using : NetworkX graph constructor, optional (default=nx.Graph)
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284 Graph type to create. If graph instance, then cleared before populated.
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285
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286 See Also
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287 --------
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288 to_pandas_edgelist
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289
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290 Examples
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291 --------
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292 Simple integer weights on edges:
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293
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294 >>> import pandas as pd
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295 >>> pd.options.display.max_columns = 20
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296 >>> import numpy as np
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297 >>> rng = np.random.RandomState(seed=5)
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298 >>> ints = rng.randint(1, 11, size=(3,2))
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299 >>> a = ['A', 'B', 'C']
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300 >>> b = ['D', 'A', 'E']
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301 >>> df = pd.DataFrame(ints, columns=['weight', 'cost'])
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302 >>> df[0] = a
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303 >>> df['b'] = b
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304 >>> df[['weight', 'cost', 0, 'b']]
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305 weight cost 0 b
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306 0 4 7 A D
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307 1 7 1 B A
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308 2 10 9 C E
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309 >>> G = nx.from_pandas_edgelist(df, 0, 'b', ['weight', 'cost'])
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310 >>> G['E']['C']['weight']
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311 10
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312 >>> G['E']['C']['cost']
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313 9
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314 >>> edges = pd.DataFrame({'source': [0, 1, 2],
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315 ... 'target': [2, 2, 3],
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316 ... 'weight': [3, 4, 5],
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317 ... 'color': ['red', 'blue', 'blue']})
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318 >>> G = nx.from_pandas_edgelist(edges, edge_attr=True)
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319 >>> G[0][2]['color']
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320 'red'
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321
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322 """
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323 g = nx.empty_graph(0, create_using)
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324
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325 if edge_attr is None:
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326 g.add_edges_from(zip(df[source], df[target]))
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327 return g
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328
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329 # Additional columns requested
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330 if edge_attr is True:
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331 cols = [c for c in df.columns if c is not source and c is not target]
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332 elif isinstance(edge_attr, (list, tuple)):
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333 cols = edge_attr
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334 else:
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335 cols = [edge_attr]
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336 if len(cols) == 0:
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337 msg = "Invalid edge_attr argument. No columns found with name: %s"
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338 raise nx.NetworkXError(msg % cols)
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339
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340 try:
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341 eattrs = zip(*[df[col] for col in cols])
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342 except (KeyError, TypeError) as e:
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343 msg = "Invalid edge_attr argument: %s" % edge_attr
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344 raise nx.NetworkXError(msg)
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345 for s, t, attrs in zip(df[source], df[target], eattrs):
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346 if g.is_multigraph():
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347 key = g.add_edge(s, t)
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348 g[s][t][key].update(zip(cols, attrs))
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349 else:
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350 g.add_edge(s, t)
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351 g[s][t].update(zip(cols, attrs))
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352
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353 return g
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354
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355
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356 def to_numpy_matrix(G, nodelist=None, dtype=None, order=None,
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357 multigraph_weight=sum, weight='weight', nonedge=0.0):
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358 """Returns the graph adjacency matrix as a NumPy matrix.
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359
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360 Parameters
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361 ----------
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362 G : graph
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363 The NetworkX graph used to construct the NumPy matrix.
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364
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365 nodelist : list, optional
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366 The rows and columns are ordered according to the nodes in `nodelist`.
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367 If `nodelist` is None, then the ordering is produced by G.nodes().
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368
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369 dtype : NumPy data type, optional
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370 A valid single NumPy data type used to initialize the array.
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371 This must be a simple type such as int or numpy.float64 and
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372 not a compound data type (see to_numpy_recarray)
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373 If None, then the NumPy default is used.
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374
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375 order : {'C', 'F'}, optional
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376 Whether to store multidimensional data in C- or Fortran-contiguous
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377 (row- or column-wise) order in memory. If None, then the NumPy default
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378 is used.
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379
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380 multigraph_weight : {sum, min, max}, optional
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381 An operator that determines how weights in multigraphs are handled.
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382 The default is to sum the weights of the multiple edges.
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383
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384 weight : string or None optional (default = 'weight')
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385 The edge attribute that holds the numerical value used for
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386 the edge weight. If an edge does not have that attribute, then the
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387 value 1 is used instead.
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388
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389 nonedge : float (default = 0.0)
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390 The matrix values corresponding to nonedges are typically set to zero.
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391 However, this could be undesirable if there are matrix values
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392 corresponding to actual edges that also have the value zero. If so,
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393 one might prefer nonedges to have some other value, such as nan.
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394
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395 Returns
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396 -------
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397 M : NumPy matrix
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398 Graph adjacency matrix
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399
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400 See Also
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401 --------
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402 to_numpy_recarray, from_numpy_matrix
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403
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404 Notes
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405 -----
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406 For directed graphs, entry i,j corresponds to an edge from i to j.
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407
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408 The matrix entries are assigned to the weight edge attribute. When
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409 an edge does not have a weight attribute, the value of the entry is set to
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410 the number 1. For multiple (parallel) edges, the values of the entries
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411 are determined by the `multigraph_weight` parameter. The default is to
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412 sum the weight attributes for each of the parallel edges.
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413
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414 When `nodelist` does not contain every node in `G`, the matrix is built
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415 from the subgraph of `G` that is induced by the nodes in `nodelist`.
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416
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417 The convention used for self-loop edges in graphs is to assign the
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418 diagonal matrix entry value to the weight attribute of the edge
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419 (or the number 1 if the edge has no weight attribute). If the
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420 alternate convention of doubling the edge weight is desired the
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421 resulting Numpy matrix can be modified as follows:
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422
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423 >>> import numpy as np
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424 >>> G = nx.Graph([(1, 1)])
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425 >>> A = nx.to_numpy_matrix(G)
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426 >>> A
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427 matrix([[1.]])
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428 >>> A[np.diag_indices_from(A)] *= 2
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429 >>> A
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430 matrix([[2.]])
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431
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432 Examples
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433 --------
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434 >>> G = nx.MultiDiGraph()
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435 >>> G.add_edge(0, 1, weight=2)
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436 0
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437 >>> G.add_edge(1, 0)
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438 0
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439 >>> G.add_edge(2, 2, weight=3)
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440 0
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441 >>> G.add_edge(2, 2)
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442 1
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443 >>> nx.to_numpy_matrix(G, nodelist=[0, 1, 2])
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444 matrix([[0., 2., 0.],
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445 [1., 0., 0.],
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446 [0., 0., 4.]])
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447
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448 """
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449 import numpy as np
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450
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451 A = to_numpy_array(G, nodelist=nodelist, dtype=dtype, order=order,
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452 multigraph_weight=multigraph_weight, weight=weight,
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453 nonedge=nonedge)
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454 M = np.asmatrix(A, dtype=dtype)
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455 return M
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456
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457
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458 def from_numpy_matrix(A, parallel_edges=False, create_using=None):
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459 """Returns a graph from numpy matrix.
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460
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461 The numpy matrix is interpreted as an adjacency matrix for the graph.
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462
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463 Parameters
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464 ----------
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465 A : numpy matrix
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466 An adjacency matrix representation of a graph
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467
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468 parallel_edges : Boolean
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469 If True, `create_using` is a multigraph, and `A` is an
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470 integer matrix, then entry *(i, j)* in the matrix is interpreted as the
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471 number of parallel edges joining vertices *i* and *j* in the graph.
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472 If False, then the entries in the adjacency matrix are interpreted as
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473 the weight of a single edge joining the vertices.
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474
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475 create_using : NetworkX graph constructor, optional (default=nx.Graph)
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476 Graph type to create. If graph instance, then cleared before populated.
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477
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478 Notes
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479 -----
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480 For directed graphs, explicitly mention create_using=nx.Digraph,
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481 and entry i,j of A corresponds to an edge from i to j.
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482
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483 If `create_using` is :class:`networkx.MultiGraph` or
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484 :class:`networkx.MultiDiGraph`, `parallel_edges` is True, and the
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485 entries of `A` are of type :class:`int`, then this function returns a
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486 multigraph (constructed from `create_using`) with parallel edges.
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487
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488 If `create_using` indicates an undirected multigraph, then only the edges
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489 indicated by the upper triangle of the matrix `A` will be added to the
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490 graph.
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491
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492 If the numpy matrix has a single data type for each matrix entry it
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493 will be converted to an appropriate Python data type.
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494
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495 If the numpy matrix has a user-specified compound data type the names
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496 of the data fields will be used as attribute keys in the resulting
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497 NetworkX graph.
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498
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499 See Also
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500 --------
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501 to_numpy_matrix, to_numpy_recarray
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502
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503 Examples
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504 --------
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505 Simple integer weights on edges:
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506
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507 >>> import numpy as np
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508 >>> A = np.array([[1, 1], [2, 1]])
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509 >>> G = nx.from_numpy_matrix(A)
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510
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511 If `create_using` indicates a multigraph and the matrix has only integer
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512 entries and `parallel_edges` is False, then the entries will be treated
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513 as weights for edges joining the nodes (without creating parallel edges):
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514
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515 >>> A = np.array([[1, 1], [1, 2]])
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516 >>> G = nx.from_numpy_matrix(A, create_using=nx.MultiGraph)
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517 >>> G[1][1]
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518 AtlasView({0: {'weight': 2}})
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519
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520 If `create_using` indicates a multigraph and the matrix has only integer
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521 entries and `parallel_edges` is True, then the entries will be treated
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522 as the number of parallel edges joining those two vertices:
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523
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524 >>> A = np.array([[1, 1], [1, 2]])
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525 >>> temp = nx.MultiGraph()
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526 >>> G = nx.from_numpy_matrix(A, parallel_edges=True, create_using=temp)
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527 >>> G[1][1]
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528 AtlasView({0: {'weight': 1}, 1: {'weight': 1}})
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529
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530 User defined compound data type on edges:
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531
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532 >>> dt = [('weight', float), ('cost', int)]
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533 >>> A = np.array([[(1.0, 2)]], dtype=dt)
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534 >>> G = nx.from_numpy_matrix(A)
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535 >>> list(G.edges())
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536 [(0, 0)]
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537 >>> G[0][0]['cost']
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538 2
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539 >>> G[0][0]['weight']
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540 1.0
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541
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542 """
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543 # This should never fail if you have created a numpy matrix with numpy...
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544 import numpy as np
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545 kind_to_python_type = {'f': float,
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546 'i': int,
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547 'u': int,
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548 'b': bool,
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549 'c': complex,
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550 'S': str,
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551 'V': 'void'}
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552 try: # Python 3.x
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553 blurb = chr(1245) # just to trigger the exception
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554 kind_to_python_type['U'] = str
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555 except ValueError: # Python 2.7
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556 kind_to_python_type['U'] = unicode
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557 G = nx.empty_graph(0, create_using)
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558 n, m = A.shape
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559 if n != m:
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560 raise nx.NetworkXError("Adjacency matrix is not square.",
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561 "nx,ny=%s" % (A.shape,))
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562 dt = A.dtype
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563 try:
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564 python_type = kind_to_python_type[dt.kind]
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565 except Exception:
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566 raise TypeError("Unknown numpy data type: %s" % dt)
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567
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568 # Make sure we get even the isolated nodes of the graph.
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569 G.add_nodes_from(range(n))
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570 # Get a list of all the entries in the matrix with nonzero entries. These
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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571 # coordinates will become the edges in the graph.
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572 edges = map(lambda e: (int(e[0]), int(e[1])),
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573 zip(*(np.asarray(A).nonzero())))
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574 # handle numpy constructed data type
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575 if python_type == 'void':
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576 # Sort the fields by their offset, then by dtype, then by name.
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577 fields = sorted((offset, dtype, name) for name, (dtype, offset) in
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578 A.dtype.fields.items())
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579 triples = ((u, v, {name: kind_to_python_type[dtype.kind](val)
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580 for (_, dtype, name), val in zip(fields, A[u, v])})
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581 for u, v in edges)
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582 # If the entries in the adjacency matrix are integers, the graph is a
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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583 # multigraph, and parallel_edges is True, then create parallel edges, each
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584 # with weight 1, for each entry in the adjacency matrix. Otherwise, create
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585 # one edge for each positive entry in the adjacency matrix and set the
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586 # weight of that edge to be the entry in the matrix.
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587 elif python_type is int and G.is_multigraph() and parallel_edges:
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588 chain = itertools.chain.from_iterable
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589 # The following line is equivalent to:
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590 #
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591 # for (u, v) in edges:
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592 # for d in range(A[u, v]):
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593 # G.add_edge(u, v, weight=1)
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594 #
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595 triples = chain(((u, v, dict(weight=1)) for d in range(A[u, v]))
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596 for (u, v) in edges)
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597 else: # basic data type
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598 triples = ((u, v, dict(weight=python_type(A[u, v])))
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599 for u, v in edges)
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600 # If we are creating an undirected multigraph, only add the edges from the
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601 # upper triangle of the matrix. Otherwise, add all the edges. This relies
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602 # on the fact that the vertices created in the
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603 # `_generated_weighted_edges()` function are actually the row/column
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diff changeset
604 # indices for the matrix `A`.
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diff changeset
605 #
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606 # Without this check, we run into a problem where each edge is added twice
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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607 # when `G.add_edges_from()` is invoked below.
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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608 if G.is_multigraph() and not G.is_directed():
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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diff changeset
609 triples = ((u, v, d) for u, v, d in triples if u <= v)
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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diff changeset
610 G.add_edges_from(triples)
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diff changeset
611 return G
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612
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613
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614 @not_implemented_for('multigraph')
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diff changeset
615 def to_numpy_recarray(G, nodelist=None, dtype=None, order=None):
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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616 """Returns the graph adjacency matrix as a NumPy recarray.
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617
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618 Parameters
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619 ----------
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620 G : graph
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621 The NetworkX graph used to construct the NumPy matrix.
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622
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623 nodelist : list, optional
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624 The rows and columns are ordered according to the nodes in `nodelist`.
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625 If `nodelist` is None, then the ordering is produced by G.nodes().
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626
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627 dtype : NumPy data-type, optional
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628 A valid NumPy named dtype used to initialize the NumPy recarray.
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629 The data type names are assumed to be keys in the graph edge attribute
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630 dictionary.
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631
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632 order : {'C', 'F'}, optional
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633 Whether to store multidimensional data in C- or Fortran-contiguous
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634 (row- or column-wise) order in memory. If None, then the NumPy default
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635 is used.
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636
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637 Returns
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638 -------
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639 M : NumPy recarray
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640 The graph with specified edge data as a Numpy recarray
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641
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642 Notes
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643 -----
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644 When `nodelist` does not contain every node in `G`, the matrix is built
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645 from the subgraph of `G` that is induced by the nodes in `nodelist`.
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646
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647 Examples
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648 --------
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649 >>> G = nx.Graph()
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650 >>> G.add_edge(1, 2, weight=7.0, cost=5)
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651 >>> A = nx.to_numpy_recarray(G, dtype=[('weight', float), ('cost', int)])
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652 >>> print(A.weight)
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653 [[0. 7.]
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654 [7. 0.]]
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655 >>> print(A.cost)
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656 [[0 5]
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657 [5 0]]
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658
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659 """
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660 if dtype is None:
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661 dtype = [('weight', float)]
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662 import numpy as np
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663 if nodelist is None:
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664 nodelist = list(G)
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665 nodeset = set(nodelist)
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666 if len(nodelist) != len(nodeset):
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667 msg = "Ambiguous ordering: `nodelist` contained duplicates."
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668 raise nx.NetworkXError(msg)
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669 nlen = len(nodelist)
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670 undirected = not G.is_directed()
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671 index = dict(zip(nodelist, range(nlen)))
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672 M = np.zeros((nlen, nlen), dtype=dtype, order=order)
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673
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674 names = M.dtype.names
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675 for u, v, attrs in G.edges(data=True):
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676 if (u in nodeset) and (v in nodeset):
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677 i, j = index[u], index[v]
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678 values = tuple([attrs[n] for n in names])
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679 M[i, j] = values
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680 if undirected:
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681 M[j, i] = M[i, j]
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682
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683 return M.view(np.recarray)
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684
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685
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686 def to_scipy_sparse_matrix(G, nodelist=None, dtype=None,
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687 weight='weight', format='csr'):
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688 """Returns the graph adjacency matrix as a SciPy sparse matrix.
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689
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690 Parameters
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691 ----------
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692 G : graph
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693 The NetworkX graph used to construct the NumPy matrix.
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694
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695 nodelist : list, optional
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696 The rows and columns are ordered according to the nodes in `nodelist`.
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697 If `nodelist` is None, then the ordering is produced by G.nodes().
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698
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699 dtype : NumPy data-type, optional
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diff changeset
700 A valid NumPy dtype used to initialize the array. If None, then the
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701 NumPy default is used.
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diff changeset
702
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703 weight : string or None optional (default='weight')
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704 The edge attribute that holds the numerical value used for
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705 the edge weight. If None then all edge weights are 1.
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706
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707 format : str in {'bsr', 'csr', 'csc', 'coo', 'lil', 'dia', 'dok'}
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diff changeset
708 The type of the matrix to be returned (default 'csr'). For
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diff changeset
709 some algorithms different implementations of sparse matrices
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diff changeset
710 can perform better. See [1]_ for details.
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711
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712 Returns
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713 -------
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714 M : SciPy sparse matrix
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diff changeset
715 Graph adjacency matrix.
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716
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diff changeset
717 Notes
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718 -----
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719 For directed graphs, matrix entry i,j corresponds to an edge from i to j.
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diff changeset
720
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diff changeset
721 The matrix entries are populated using the edge attribute held in
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diff changeset
722 parameter weight. When an edge does not have that attribute, the
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diff changeset
723 value of the entry is 1.
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diff changeset
724
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diff changeset
725 For multiple edges the matrix values are the sums of the edge weights.
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diff changeset
726
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diff changeset
727 When `nodelist` does not contain every node in `G`, the matrix is built
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diff changeset
728 from the subgraph of `G` that is induced by the nodes in `nodelist`.
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diff changeset
729
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730 Uses coo_matrix format. To convert to other formats specify the
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diff changeset
731 format= keyword.
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diff changeset
732
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diff changeset
733 The convention used for self-loop edges in graphs is to assign the
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diff changeset
734 diagonal matrix entry value to the weight attribute of the edge
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diff changeset
735 (or the number 1 if the edge has no weight attribute). If the
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diff changeset
736 alternate convention of doubling the edge weight is desired the
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diff changeset
737 resulting Scipy sparse matrix can be modified as follows:
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738
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739 >>> import scipy as sp
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740 >>> G = nx.Graph([(1, 1)])
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parents:
diff changeset
741 >>> A = nx.to_scipy_sparse_matrix(G)
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diff changeset
742 >>> print(A.todense())
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diff changeset
743 [[1]]
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744 >>> A.setdiag(A.diagonal() * 2)
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745 >>> print(A.todense())
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parents:
diff changeset
746 [[2]]
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747
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748 Examples
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749 --------
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750 >>> G = nx.MultiDiGraph()
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diff changeset
751 >>> G.add_edge(0, 1, weight=2)
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752 0
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diff changeset
753 >>> G.add_edge(1, 0)
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diff changeset
754 0
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diff changeset
755 >>> G.add_edge(2, 2, weight=3)
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756 0
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diff changeset
757 >>> G.add_edge(2, 2)
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758 1
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759 >>> S = nx.to_scipy_sparse_matrix(G, nodelist=[0, 1, 2])
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diff changeset
760 >>> print(S.todense())
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parents:
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761 [[0 2 0]
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762 [1 0 0]
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763 [0 0 4]]
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764
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765 References
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766 ----------
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767 .. [1] Scipy Dev. References, "Sparse Matrices",
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diff changeset
768 https://docs.scipy.org/doc/scipy/reference/sparse.html
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769 """
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diff changeset
770 from scipy import sparse
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
771 if nodelist is None:
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
772 nodelist = list(G)
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
773 nlen = len(nodelist)
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
774 if nlen == 0:
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
775 raise nx.NetworkXError("Graph has no nodes or edges")
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
776
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
777 if len(nodelist) != len(set(nodelist)):
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
778 msg = "Ambiguous ordering: `nodelist` contained duplicates."
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
779 raise nx.NetworkXError(msg)
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
780
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
781 index = dict(zip(nodelist, range(nlen)))
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
782 coefficients = zip(*((index[u], index[v], d.get(weight, 1))
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
783 for u, v, d in G.edges(nodelist, data=True)
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
784 if u in index and v in index))
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
785 try:
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
786 row, col, data = coefficients
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
787 except ValueError:
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
788 # there is no edge in the subgraph
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
789 row, col, data = [], [], []
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
790
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
791 if G.is_directed():
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
792 M = sparse.coo_matrix((data, (row, col)),
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
793 shape=(nlen, nlen), dtype=dtype)
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
794 else:
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
795 # symmetrize matrix
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
796 d = data + data
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
797 r = row + col
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
798 c = col + row
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
799 # selfloop entries get double counted when symmetrizing
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
800 # so we subtract the data on the diagonal
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
801 selfloops = list(nx.selfloop_edges(G, data=True))
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
802 if selfloops:
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
803 diag_index, diag_data = zip(*((index[u], -d.get(weight, 1))
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
804 for u, v, d in selfloops
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
805 if u in index and v in index))
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
806 d += diag_data
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
807 r += diag_index
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
808 c += diag_index
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
809 M = sparse.coo_matrix((d, (r, c)), shape=(nlen, nlen), dtype=dtype)
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
810 try:
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
811 return M.asformat(format)
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
812 # From Scipy 1.1.0, asformat will throw a ValueError instead of an
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
813 # AttributeError if the format if not recognized.
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
814 except (AttributeError, ValueError):
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
815 raise nx.NetworkXError("Unknown sparse matrix format: %s" % format)
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
816
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
817
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
818 def _csr_gen_triples(A):
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
819 """Converts a SciPy sparse matrix in **Compressed Sparse Row** format to
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
820 an iterable of weighted edge triples.
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
821
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
822 """
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
823 nrows = A.shape[0]
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
824 data, indices, indptr = A.data, A.indices, A.indptr
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
825 for i in range(nrows):
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
826 for j in range(indptr[i], indptr[i + 1]):
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
827 yield i, indices[j], data[j]
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
828
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
829
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
830 def _csc_gen_triples(A):
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
831 """Converts a SciPy sparse matrix in **Compressed Sparse Column** format to
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
832 an iterable of weighted edge triples.
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
833
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
834 """
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
835 ncols = A.shape[1]
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
836 data, indices, indptr = A.data, A.indices, A.indptr
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
837 for i in range(ncols):
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
838 for j in range(indptr[i], indptr[i + 1]):
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
839 yield indices[j], i, data[j]
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
840
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
841
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
842 def _coo_gen_triples(A):
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
843 """Converts a SciPy sparse matrix in **Coordinate** format to an iterable
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
844 of weighted edge triples.
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
845
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
846 """
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
847 row, col, data = A.row, A.col, A.data
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
848 return zip(row, col, data)
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
849
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
850
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
851 def _dok_gen_triples(A):
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
852 """Converts a SciPy sparse matrix in **Dictionary of Keys** format to an
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
853 iterable of weighted edge triples.
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
854
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
855 """
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
856 for (r, c), v in A.items():
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
857 yield r, c, v
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
858
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
859
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
860 def _generate_weighted_edges(A):
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
861 """Returns an iterable over (u, v, w) triples, where u and v are adjacent
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
862 vertices and w is the weight of the edge joining u and v.
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
863
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
864 `A` is a SciPy sparse matrix (in any format).
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
865
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
866 """
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
867 if A.format == 'csr':
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
868 return _csr_gen_triples(A)
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
869 if A.format == 'csc':
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
870 return _csc_gen_triples(A)
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
871 if A.format == 'dok':
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
872 return _dok_gen_triples(A)
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
873 # If A is in any other format (including COO), convert it to COO format.
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
874 return _coo_gen_triples(A.tocoo())
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
875
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
876
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
877 def from_scipy_sparse_matrix(A, parallel_edges=False, create_using=None,
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
878 edge_attribute='weight'):
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
879 """Creates a new graph from an adjacency matrix given as a SciPy sparse
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
880 matrix.
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
881
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
882 Parameters
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
883 ----------
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
884 A: scipy sparse matrix
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
885 An adjacency matrix representation of a graph
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
886
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
887 parallel_edges : Boolean
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
888 If this is True, `create_using` is a multigraph, and `A` is an
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
889 integer matrix, then entry *(i, j)* in the matrix is interpreted as the
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
890 number of parallel edges joining vertices *i* and *j* in the graph.
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
891 If it is False, then the entries in the matrix are interpreted as
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
892 the weight of a single edge joining the vertices.
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
893
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
894 create_using : NetworkX graph constructor, optional (default=nx.Graph)
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
895 Graph type to create. If graph instance, then cleared before populated.
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
896
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
897 edge_attribute: string
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
898 Name of edge attribute to store matrix numeric value. The data will
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diff changeset
899 have the same type as the matrix entry (int, float, (real,imag)).
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900
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diff changeset
901 Notes
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diff changeset
902 -----
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diff changeset
903 For directed graphs, explicitly mention create_using=nx.Digraph,
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parents:
diff changeset
904 and entry i,j of A corresponds to an edge from i to j.
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diff changeset
905
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diff changeset
906 If `create_using` is :class:`networkx.MultiGraph` or
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diff changeset
907 :class:`networkx.MultiDiGraph`, `parallel_edges` is True, and the
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diff changeset
908 entries of `A` are of type :class:`int`, then this function returns a
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diff changeset
909 multigraph (constructed from `create_using`) with parallel edges.
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parents:
diff changeset
910 In this case, `edge_attribute` will be ignored.
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911
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diff changeset
912 If `create_using` indicates an undirected multigraph, then only the edges
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parents:
diff changeset
913 indicated by the upper triangle of the matrix `A` will be added to the
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parents:
diff changeset
914 graph.
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diff changeset
915
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diff changeset
916 Examples
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917 --------
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918 >>> import scipy as sp
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diff changeset
919 >>> A = sp.sparse.eye(2, 2, 1)
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diff changeset
920 >>> G = nx.from_scipy_sparse_matrix(A)
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diff changeset
921
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922 If `create_using` indicates a multigraph and the matrix has only integer
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diff changeset
923 entries and `parallel_edges` is False, then the entries will be treated
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924 as weights for edges joining the nodes (without creating parallel edges):
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diff changeset
925
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diff changeset
926 >>> A = sp.sparse.csr_matrix([[1, 1], [1, 2]])
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parents:
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927 >>> G = nx.from_scipy_sparse_matrix(A, create_using=nx.MultiGraph)
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diff changeset
928 >>> G[1][1]
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diff changeset
929 AtlasView({0: {'weight': 2}})
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diff changeset
930
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parents:
diff changeset
931 If `create_using` indicates a multigraph and the matrix has only integer
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parents:
diff changeset
932 entries and `parallel_edges` is True, then the entries will be treated
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diff changeset
933 as the number of parallel edges joining those two vertices:
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diff changeset
934
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diff changeset
935 >>> A = sp.sparse.csr_matrix([[1, 1], [1, 2]])
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936 >>> G = nx.from_scipy_sparse_matrix(A, parallel_edges=True,
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937 ... create_using=nx.MultiGraph)
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parents:
diff changeset
938 >>> G[1][1]
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diff changeset
939 AtlasView({0: {'weight': 1}, 1: {'weight': 1}})
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parents:
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940
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941 """
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diff changeset
942 G = nx.empty_graph(0, create_using)
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diff changeset
943 n, m = A.shape
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diff changeset
944 if n != m:
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diff changeset
945 raise nx.NetworkXError(
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parents:
diff changeset
946 "Adjacency matrix is not square. nx,ny=%s" % (A.shape,))
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diff changeset
947 # Make sure we get even the isolated nodes of the graph.
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parents:
diff changeset
948 G.add_nodes_from(range(n))
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diff changeset
949 # Create an iterable over (u, v, w) triples and for each triple, add an
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diff changeset
950 # edge from u to v with weight w.
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diff changeset
951 triples = _generate_weighted_edges(A)
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diff changeset
952 # If the entries in the adjacency matrix are integers, the graph is a
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diff changeset
953 # multigraph, and parallel_edges is True, then create parallel edges, each
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diff changeset
954 # with weight 1, for each entry in the adjacency matrix. Otherwise, create
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diff changeset
955 # one edge for each positive entry in the adjacency matrix and set the
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diff changeset
956 # weight of that edge to be the entry in the matrix.
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diff changeset
957 if A.dtype.kind in ('i', 'u') and G.is_multigraph() and parallel_edges:
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958 chain = itertools.chain.from_iterable
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959 # The following line is equivalent to:
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960 #
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961 # for (u, v) in edges:
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962 # for d in range(A[u, v]):
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963 # G.add_edge(u, v, weight=1)
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964 #
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965 triples = chain(((u, v, 1) for d in range(w)) for (u, v, w) in triples)
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966 # If we are creating an undirected multigraph, only add the edges from the
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diff changeset
967 # upper triangle of the matrix. Otherwise, add all the edges. This relies
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diff changeset
968 # on the fact that the vertices created in the
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969 # `_generated_weighted_edges()` function are actually the row/column
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diff changeset
970 # indices for the matrix `A`.
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diff changeset
971 #
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972 # Without this check, we run into a problem where each edge is added twice
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973 # when `G.add_weighted_edges_from()` is invoked below.
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diff changeset
974 if G.is_multigraph() and not G.is_directed():
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diff changeset
975 triples = ((u, v, d) for u, v, d in triples if u <= v)
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diff changeset
976 G.add_weighted_edges_from(triples, weight=edge_attribute)
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parents:
diff changeset
977 return G
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diff changeset
978
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diff changeset
979
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980 def to_numpy_array(G, nodelist=None, dtype=None, order=None,
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diff changeset
981 multigraph_weight=sum, weight='weight', nonedge=0.0):
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diff changeset
982 """Returns the graph adjacency matrix as a NumPy array.
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diff changeset
983
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984 Parameters
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diff changeset
985 ----------
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diff changeset
986 G : graph
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diff changeset
987 The NetworkX graph used to construct the NumPy array.
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diff changeset
988
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diff changeset
989 nodelist : list, optional
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diff changeset
990 The rows and columns are ordered according to the nodes in `nodelist`.
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diff changeset
991 If `nodelist` is None, then the ordering is produced by G.nodes().
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diff changeset
992
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diff changeset
993 dtype : NumPy data type, optional
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diff changeset
994 A valid single NumPy data type used to initialize the array.
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parents:
diff changeset
995 This must be a simple type such as int or numpy.float64 and
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parents:
diff changeset
996 not a compound data type (see to_numpy_recarray)
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diff changeset
997 If None, then the NumPy default is used.
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diff changeset
998
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diff changeset
999 order : {'C', 'F'}, optional
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diff changeset
1000 Whether to store multidimensional data in C- or Fortran-contiguous
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diff changeset
1001 (row- or column-wise) order in memory. If None, then the NumPy default
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diff changeset
1002 is used.
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diff changeset
1003
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1004 multigraph_weight : {sum, min, max}, optional
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diff changeset
1005 An operator that determines how weights in multigraphs are handled.
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diff changeset
1006 The default is to sum the weights of the multiple edges.
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diff changeset
1007
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diff changeset
1008 weight : string or None optional (default = 'weight')
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diff changeset
1009 The edge attribute that holds the numerical value used for
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diff changeset
1010 the edge weight. If an edge does not have that attribute, then the
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1011 value 1 is used instead.
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diff changeset
1012
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diff changeset
1013 nonedge : float (default = 0.0)
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diff changeset
1014 The array values corresponding to nonedges are typically set to zero.
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diff changeset
1015 However, this could be undesirable if there are array values
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diff changeset
1016 corresponding to actual edges that also have the value zero. If so,
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diff changeset
1017 one might prefer nonedges to have some other value, such as nan.
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1018
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1019 Returns
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1020 -------
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diff changeset
1021 A : NumPy ndarray
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parents:
diff changeset
1022 Graph adjacency matrix
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parents:
diff changeset
1023
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parents:
diff changeset
1024 See Also
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parents:
diff changeset
1025 --------
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parents:
diff changeset
1026 from_numpy_array
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parents:
diff changeset
1027
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parents:
diff changeset
1028 Notes
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1029 -----
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parents:
diff changeset
1030 For directed graphs, entry i,j corresponds to an edge from i to j.
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parents:
diff changeset
1031
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parents:
diff changeset
1032 Entries in the adjacency matrix are assigned to the weight edge attribute.
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1033 When an edge does not have a weight attribute, the value of the entry is
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1034 set to the number 1. For multiple (parallel) edges, the values of the
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1035 entries are determined by the `multigraph_weight` parameter. The default is
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1036 to sum the weight attributes for each of the parallel edges.
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parents:
diff changeset
1037
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parents:
diff changeset
1038 When `nodelist` does not contain every node in `G`, the adjacency matrix is
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
1039 built from the subgraph of `G` that is induced by the nodes in `nodelist`.
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parents:
diff changeset
1040
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parents:
diff changeset
1041 The convention used for self-loop edges in graphs is to assign the
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1042 diagonal array entry value to the weight attribute of the edge
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parents:
diff changeset
1043 (or the number 1 if the edge has no weight attribute). If the
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1044 alternate convention of doubling the edge weight is desired the
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1045 resulting NumPy array can be modified as follows:
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parents:
diff changeset
1046
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parents:
diff changeset
1047 >>> import numpy as np
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parents:
diff changeset
1048 >>> G = nx.Graph([(1, 1)])
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parents:
diff changeset
1049 >>> A = nx.to_numpy_array(G)
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parents:
diff changeset
1050 >>> A
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parents:
diff changeset
1051 array([[1.]])
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parents:
diff changeset
1052 >>> A[np.diag_indices_from(A)] *= 2
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parents:
diff changeset
1053 >>> A
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parents:
diff changeset
1054 array([[2.]])
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parents:
diff changeset
1055
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parents:
diff changeset
1056 Examples
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parents:
diff changeset
1057 --------
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parents:
diff changeset
1058 >>> G = nx.MultiDiGraph()
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parents:
diff changeset
1059 >>> G.add_edge(0, 1, weight=2)
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parents:
diff changeset
1060 0
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parents:
diff changeset
1061 >>> G.add_edge(1, 0)
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parents:
diff changeset
1062 0
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parents:
diff changeset
1063 >>> G.add_edge(2, 2, weight=3)
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parents:
diff changeset
1064 0
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parents:
diff changeset
1065 >>> G.add_edge(2, 2)
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parents:
diff changeset
1066 1
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parents:
diff changeset
1067 >>> nx.to_numpy_array(G, nodelist=[0, 1, 2])
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parents:
diff changeset
1068 array([[0., 2., 0.],
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parents:
diff changeset
1069 [1., 0., 0.],
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parents:
diff changeset
1070 [0., 0., 4.]])
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parents:
diff changeset
1071
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parents:
diff changeset
1072 """
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parents:
diff changeset
1073 import numpy as np
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parents:
diff changeset
1074
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parents:
diff changeset
1075 if nodelist is None:
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parents:
diff changeset
1076 nodelist = list(G)
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parents:
diff changeset
1077 nodeset = set(nodelist)
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parents:
diff changeset
1078 if len(nodelist) != len(nodeset):
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parents:
diff changeset
1079 msg = "Ambiguous ordering: `nodelist` contained duplicates."
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1080 raise nx.NetworkXError(msg)
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parents:
diff changeset
1081
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parents:
diff changeset
1082 nlen = len(nodelist)
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parents:
diff changeset
1083 undirected = not G.is_directed()
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parents:
diff changeset
1084 index = dict(zip(nodelist, range(nlen)))
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parents:
diff changeset
1085
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parents:
diff changeset
1086 # Initially, we start with an array of nans. Then we populate the array
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parents:
diff changeset
1087 # using data from the graph. Afterwards, any leftover nans will be
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1088 # converted to the value of `nonedge`. Note, we use nans initially,
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parents:
diff changeset
1089 # instead of zero, for two reasons:
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parents:
diff changeset
1090 #
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1091 # 1) It can be important to distinguish a real edge with the value 0
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1092 # from a nonedge with the value 0.
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parents:
diff changeset
1093 #
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parents:
diff changeset
1094 # 2) When working with multi(di)graphs, we must combine the values of all
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1095 # edges between any two nodes in some manner. This often takes the
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1096 # form of a sum, min, or max. Using the value 0 for a nonedge would
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1097 # have undesirable effects with min and max, but using nanmin and
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parents:
diff changeset
1098 # nanmax with initially nan values is not problematic at all.
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parents:
diff changeset
1099 #
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parents:
diff changeset
1100 # That said, there are still some drawbacks to this approach. Namely, if
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1101 # a real edge is nan, then that value is a) not distinguishable from
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1102 # nonedges and b) is ignored by the default combinator (nansum, nanmin,
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1103 # nanmax) functions used for multi(di)graphs. If this becomes an issue,
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1104 # an alternative approach is to use masked arrays. Initially, every
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
1105 # element is masked and set to some `initial` value. As we populate the
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1106 # graph, elements are unmasked (automatically) when we combine the initial
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1107 # value with the values given by real edges. At the end, we convert all
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1108 # masked values to `nonedge`. Using masked arrays fully addresses reason 1,
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
1109 # but for reason 2, we would still have the issue with min and max if the
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
1110 # initial values were 0.0. Note: an initial value of +inf is appropriate
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1111 # for min, while an initial value of -inf is appropriate for max. When
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
1112 # working with sum, an initial value of zero is appropriate. Ideally then,
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
1113 # we'd want to allow users to specify both a value for nonedges and also
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
1114 # an initial value. For multi(di)graphs, the choice of the initial value
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
1115 # will, in general, depend on the combinator function---sensible defaults
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1116 # can be provided.
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parents:
diff changeset
1117
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1118 if G.is_multigraph():
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1119 # Handle MultiGraphs and MultiDiGraphs
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parents:
diff changeset
1120 A = np.full((nlen, nlen), np.nan, order=order)
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1121 # use numpy nan-aware operations
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1122 operator = {sum: np.nansum, min: np.nanmin, max: np.nanmax}
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1123 try:
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1124 op = operator[multigraph_weight]
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1125 except Exception:
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1126 raise ValueError('multigraph_weight must be sum, min, or max')
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parents:
diff changeset
1127
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parents:
diff changeset
1128 for u, v, attrs in G.edges(data=True):
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
1129 if (u in nodeset) and (v in nodeset):
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
1130 i, j = index[u], index[v]
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1131 e_weight = attrs.get(weight, 1)
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1132 A[i, j] = op([e_weight, A[i, j]])
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
1133 if undirected:
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
1134 A[j, i] = A[i, j]
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1135 else:
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1136 # Graph or DiGraph, this is much faster than above
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
1137 A = np.full((nlen, nlen), np.nan, order=order)
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
1138 for u, nbrdict in G.adjacency():
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
1139 for v, d in nbrdict.items():
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1140 try:
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1141 A[index[u], index[v]] = d.get(weight, 1)
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1142 except KeyError:
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
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parents:
diff changeset
1143 # This occurs when there are fewer desired nodes than
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
diff changeset
1144 # there are nodes in the graph: len(nodelist) < len(G)
26e78fe6e8c4 "planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
shellac
parents:
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1145 pass
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1146
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1147 A[np.isnan(A)] = nonedge
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1148 A = np.asarray(A, dtype=dtype)
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1149 return A
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1150
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1151
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1152 def from_numpy_array(A, parallel_edges=False, create_using=None):
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1153 """Returns a graph from NumPy array.
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1154
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1155 The NumPy array is interpreted as an adjacency matrix for the graph.
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1156
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1157 Parameters
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1158 ----------
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1159 A : NumPy ndarray
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1160 An adjacency matrix representation of a graph
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1161
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1162 parallel_edges : Boolean
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1163 If this is True, `create_using` is a multigraph, and `A` is an
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1164 integer array, then entry *(i, j)* in the array is interpreted as the
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1165 number of parallel edges joining vertices *i* and *j* in the graph.
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1166 If it is False, then the entries in the array are interpreted as
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1167 the weight of a single edge joining the vertices.
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1168
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1169 create_using : NetworkX graph constructor, optional (default=nx.Graph)
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1170 Graph type to create. If graph instance, then cleared before populated.
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1171
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1172 Notes
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1173 -----
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1174 For directed graphs, explicitly mention create_using=nx.Digraph,
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1175 and entry i,j of A corresponds to an edge from i to j.
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1176
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1177 If `create_using` is :class:`networkx.MultiGraph` or
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1178 :class:`networkx.MultiDiGraph`, `parallel_edges` is True, and the
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1179 entries of `A` are of type :class:`int`, then this function returns a
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1180 multigraph (of the same type as `create_using`) with parallel edges.
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1181
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1182 If `create_using` indicates an undirected multigraph, then only the edges
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1183 indicated by the upper triangle of the array `A` will be added to the
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1184 graph.
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1185
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1186 If the NumPy array has a single data type for each array entry it
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1187 will be converted to an appropriate Python data type.
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1188
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1189 If the NumPy array has a user-specified compound data type the names
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1190 of the data fields will be used as attribute keys in the resulting
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1191 NetworkX graph.
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1192
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1193 See Also
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1194 --------
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1195 to_numpy_array
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1196
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1197 Examples
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1198 --------
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1199 Simple integer weights on edges:
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1200
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1201 >>> import numpy as np
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1202 >>> A = np.array([[1, 1], [2, 1]])
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1203 >>> G = nx.from_numpy_array(A)
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1204 >>> G.edges(data=True)
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1205 EdgeDataView([(0, 0, {'weight': 1}), (0, 1, {'weight': 2}), \
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1206 (1, 1, {'weight': 1})])
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1207
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1208 If `create_using` indicates a multigraph and the array has only integer
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1209 entries and `parallel_edges` is False, then the entries will be treated
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1210 as weights for edges joining the nodes (without creating parallel edges):
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1211
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1212 >>> A = np.array([[1, 1], [1, 2]])
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1213 >>> G = nx.from_numpy_array(A, create_using=nx.MultiGraph)
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1214 >>> G[1][1]
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1215 AtlasView({0: {'weight': 2}})
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1216
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1217 If `create_using` indicates a multigraph and the array has only integer
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1218 entries and `parallel_edges` is True, then the entries will be treated
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1219 as the number of parallel edges joining those two vertices:
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1220
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1221 >>> A = np.array([[1, 1], [1, 2]])
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1222 >>> temp = nx.MultiGraph()
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1223 >>> G = nx.from_numpy_array(A, parallel_edges=True, create_using=temp)
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1224 >>> G[1][1]
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1225 AtlasView({0: {'weight': 1}, 1: {'weight': 1}})
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1226
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1227 User defined compound data type on edges:
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1228
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1229 >>> dt = [('weight', float), ('cost', int)]
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1230 >>> A = np.array([[(1.0, 2)]], dtype=dt)
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1231 >>> G = nx.from_numpy_array(A)
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1232 >>> G.edges()
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1233 EdgeView([(0, 0)])
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1234 >>> G[0][0]['cost']
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1235 2
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1236 >>> G[0][0]['weight']
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1237 1.0
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1238
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1239 """
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1240 return from_numpy_matrix(A, parallel_edges=parallel_edges,
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1241 create_using=create_using)
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1242
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1243
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1244 # fixture for pytest
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1245 def setup_module(module):
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1246 import pytest
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1247 numpy = pytest.importorskip('numpy')
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1248 scipy = pytest.importorskip('scipy')
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1249 pandas = pytest.importorskip('pandas')