Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/convert_matrix.py @ 0:4f3585e2f14b draft default tip
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
author | shellac |
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date | Mon, 22 Mar 2021 18:12:50 +0000 |
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1 """Functions to convert NetworkX graphs to and from common data containers |
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2 like numpy arrays, scipy sparse matrices, and pandas DataFrames. |
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3 |
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4 The preferred way of converting data to a NetworkX graph is through the |
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5 graph constructor. The constructor calls the to_networkx_graph() function |
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6 which attempts to guess the input type and convert it automatically. |
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7 |
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8 Examples |
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9 -------- |
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10 Create a 10 node random graph from a numpy array |
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11 |
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12 >>> import numpy as np |
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13 >>> a = np.random.randint(0, 2, size=(10, 10)) |
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14 >>> D = nx.DiGraph(a) |
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15 |
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16 or equivalently |
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17 |
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18 >>> D = nx.to_networkx_graph(a, create_using=nx.DiGraph) |
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19 |
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20 See Also |
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21 -------- |
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22 nx_agraph, nx_pydot |
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23 """ |
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24 |
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25 import itertools |
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26 import networkx as nx |
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27 from networkx.utils import not_implemented_for |
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28 |
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29 __all__ = [ |
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30 "from_numpy_matrix", |
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31 "to_numpy_matrix", |
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32 "from_pandas_adjacency", |
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33 "to_pandas_adjacency", |
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34 "from_pandas_edgelist", |
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35 "to_pandas_edgelist", |
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36 "to_numpy_recarray", |
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37 "from_scipy_sparse_matrix", |
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38 "to_scipy_sparse_matrix", |
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39 "from_numpy_array", |
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40 "to_numpy_array", |
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41 ] |
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42 |
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43 |
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44 def to_pandas_adjacency( |
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45 G, |
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46 nodelist=None, |
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47 dtype=None, |
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48 order=None, |
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49 multigraph_weight=sum, |
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50 weight="weight", |
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51 nonedge=0.0, |
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52 ): |
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53 """Returns the graph adjacency matrix as a Pandas DataFrame. |
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54 |
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55 Parameters |
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56 ---------- |
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57 G : graph |
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58 The NetworkX graph used to construct the Pandas DataFrame. |
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59 |
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60 nodelist : list, optional |
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61 The rows and columns are ordered according to the nodes in `nodelist`. |
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62 If `nodelist` is None, then the ordering is produced by G.nodes(). |
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63 |
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64 multigraph_weight : {sum, min, max}, optional |
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65 An operator that determines how weights in multigraphs are handled. |
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66 The default is to sum the weights of the multiple edges. |
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67 |
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68 weight : string or None, optional |
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69 The edge attribute that holds the numerical value used for |
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70 the edge weight. If an edge does not have that attribute, then the |
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71 value 1 is used instead. |
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72 |
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73 nonedge : float, optional |
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74 The matrix values corresponding to nonedges are typically set to zero. |
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75 However, this could be undesirable if there are matrix values |
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76 corresponding to actual edges that also have the value zero. If so, |
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77 one might prefer nonedges to have some other value, such as nan. |
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78 |
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79 Returns |
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80 ------- |
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81 df : Pandas DataFrame |
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82 Graph adjacency matrix |
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83 |
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84 Notes |
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85 ----- |
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86 For directed graphs, entry i,j corresponds to an edge from i to j. |
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87 |
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88 The DataFrame entries are assigned to the weight edge attribute. When |
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89 an edge does not have a weight attribute, the value of the entry is set to |
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90 the number 1. For multiple (parallel) edges, the values of the entries |
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91 are determined by the 'multigraph_weight' parameter. The default is to |
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92 sum the weight attributes for each of the parallel edges. |
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93 |
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94 When `nodelist` does not contain every node in `G`, the matrix is built |
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95 from the subgraph of `G` that is induced by the nodes in `nodelist`. |
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96 |
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97 The convention used for self-loop edges in graphs is to assign the |
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98 diagonal matrix entry value to the weight attribute of the edge |
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99 (or the number 1 if the edge has no weight attribute). If the |
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100 alternate convention of doubling the edge weight is desired the |
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101 resulting Pandas DataFrame can be modified as follows: |
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102 |
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103 >>> import pandas as pd |
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104 >>> pd.options.display.max_columns = 20 |
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105 >>> import numpy as np |
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106 >>> G = nx.Graph([(1, 1)]) |
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107 >>> df = nx.to_pandas_adjacency(G, dtype=int) |
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108 >>> df |
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109 1 |
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110 1 1 |
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111 >>> df.values[np.diag_indices_from(df)] *= 2 |
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112 >>> df |
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113 1 |
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114 1 2 |
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115 |
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116 Examples |
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117 -------- |
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118 >>> G = nx.MultiDiGraph() |
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119 >>> G.add_edge(0, 1, weight=2) |
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120 0 |
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121 >>> G.add_edge(1, 0) |
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122 0 |
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123 >>> G.add_edge(2, 2, weight=3) |
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124 0 |
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125 >>> G.add_edge(2, 2) |
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126 1 |
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127 >>> nx.to_pandas_adjacency(G, nodelist=[0, 1, 2], dtype=int) |
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128 0 1 2 |
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129 0 0 2 0 |
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130 1 1 0 0 |
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131 2 0 0 4 |
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132 |
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133 """ |
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134 import pandas as pd |
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135 |
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136 M = to_numpy_array( |
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137 G, |
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138 nodelist=nodelist, |
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139 dtype=dtype, |
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140 order=order, |
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141 multigraph_weight=multigraph_weight, |
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142 weight=weight, |
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143 nonedge=nonedge, |
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144 ) |
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145 if nodelist is None: |
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146 nodelist = list(G) |
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147 return pd.DataFrame(data=M, index=nodelist, columns=nodelist) |
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148 |
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149 |
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150 def from_pandas_adjacency(df, create_using=None): |
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151 r"""Returns a graph from Pandas DataFrame. |
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152 |
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153 The Pandas DataFrame is interpreted as an adjacency matrix for the graph. |
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154 |
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155 Parameters |
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156 ---------- |
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157 df : Pandas DataFrame |
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158 An adjacency matrix representation of a graph |
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159 |
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160 create_using : NetworkX graph constructor, optional (default=nx.Graph) |
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161 Graph type to create. If graph instance, then cleared before populated. |
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162 |
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163 Notes |
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164 ----- |
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165 For directed graphs, explicitly mention create_using=nx.DiGraph, |
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166 and entry i,j of df corresponds to an edge from i to j. |
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167 |
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168 If `df` has a single data type for each entry it will be converted to an |
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169 appropriate Python data type. |
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170 |
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171 If `df` has a user-specified compound data type the names |
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172 of the data fields will be used as attribute keys in the resulting |
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173 NetworkX graph. |
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174 |
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175 See Also |
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176 -------- |
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177 to_pandas_adjacency |
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178 |
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179 Examples |
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180 -------- |
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181 Simple integer weights on edges: |
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182 |
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183 >>> import pandas as pd |
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184 >>> pd.options.display.max_columns = 20 |
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185 >>> df = pd.DataFrame([[1, 1], [2, 1]]) |
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186 >>> df |
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187 0 1 |
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188 0 1 1 |
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189 1 2 1 |
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190 >>> G = nx.from_pandas_adjacency(df) |
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191 >>> G.name = "Graph from pandas adjacency matrix" |
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192 >>> print(nx.info(G)) |
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193 Name: Graph from pandas adjacency matrix |
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194 Type: Graph |
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195 Number of nodes: 2 |
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196 Number of edges: 3 |
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197 Average degree: 3.0000 |
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198 |
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199 """ |
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200 |
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201 try: |
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202 df = df[df.index] |
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203 except Exception as e: |
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204 missing = list(set(df.index).difference(set(df.columns))) |
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205 msg = f"{missing} not in columns" |
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206 raise nx.NetworkXError("Columns must match Indices.", msg) from e |
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207 |
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208 A = df.values |
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209 G = from_numpy_array(A, create_using=create_using) |
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210 |
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211 nx.relabel.relabel_nodes(G, dict(enumerate(df.columns)), copy=False) |
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212 return G |
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213 |
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214 |
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215 def to_pandas_edgelist( |
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216 G, source="source", target="target", nodelist=None, dtype=None, order=None |
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217 ): |
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218 """Returns the graph edge list as a Pandas DataFrame. |
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219 |
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220 Parameters |
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221 ---------- |
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222 G : graph |
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223 The NetworkX graph used to construct the Pandas DataFrame. |
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224 |
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225 source : str or int, optional |
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226 A valid column name (string or integer) for the source nodes (for the |
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227 directed case). |
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228 |
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229 target : str or int, optional |
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230 A valid column name (string or integer) for the target nodes (for the |
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231 directed case). |
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232 |
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233 nodelist : list, optional |
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234 Use only nodes specified in nodelist |
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235 |
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236 Returns |
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237 ------- |
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238 df : Pandas DataFrame |
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239 Graph edge list |
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240 |
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241 Examples |
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242 -------- |
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243 >>> G = nx.Graph( |
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244 ... [ |
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245 ... ("A", "B", {"cost": 1, "weight": 7}), |
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246 ... ("C", "E", {"cost": 9, "weight": 10}), |
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247 ... ] |
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248 ... ) |
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249 >>> df = nx.to_pandas_edgelist(G, nodelist=["A", "C"]) |
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250 >>> df[["source", "target", "cost", "weight"]] |
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251 source target cost weight |
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252 0 A B 1 7 |
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253 1 C E 9 10 |
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254 |
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255 """ |
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256 import pandas as pd |
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257 |
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258 if nodelist is None: |
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259 edgelist = G.edges(data=True) |
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260 else: |
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261 edgelist = G.edges(nodelist, data=True) |
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262 source_nodes = [s for s, t, d in edgelist] |
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263 target_nodes = [t for s, t, d in edgelist] |
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264 |
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265 all_keys = set().union(*(d.keys() for s, t, d in edgelist)) |
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266 if source in all_keys: |
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267 raise nx.NetworkXError(f"Source name '{source}' is an edge attr name") |
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268 if target in all_keys: |
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269 raise nx.NetworkXError(f"Target name '{target}' is an edge attr name") |
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270 |
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271 nan = float("nan") |
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272 edge_attr = {k: [d.get(k, nan) for s, t, d in edgelist] for k in all_keys} |
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273 |
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274 edgelistdict = {source: source_nodes, target: target_nodes} |
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275 edgelistdict.update(edge_attr) |
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276 return pd.DataFrame(edgelistdict) |
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277 |
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278 |
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279 def from_pandas_edgelist( |
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280 df, |
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281 source="source", |
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282 target="target", |
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283 edge_attr=None, |
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284 create_using=None, |
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285 edge_key=None, |
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286 ): |
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287 """Returns a graph from Pandas DataFrame containing an edge list. |
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288 |
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289 The Pandas DataFrame should contain at least two columns of node names and |
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290 zero or more columns of edge attributes. Each row will be processed as one |
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291 edge instance. |
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292 |
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293 Note: This function iterates over DataFrame.values, which is not |
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294 guaranteed to retain the data type across columns in the row. This is only |
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295 a problem if your row is entirely numeric and a mix of ints and floats. In |
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296 that case, all values will be returned as floats. See the |
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297 DataFrame.iterrows documentation for an example. |
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298 |
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299 Parameters |
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300 ---------- |
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301 df : Pandas DataFrame |
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302 An edge list representation of a graph |
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303 |
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304 source : str or int |
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305 A valid column name (string or integer) for the source nodes (for the |
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306 directed case). |
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307 |
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308 target : str or int |
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309 A valid column name (string or integer) for the target nodes (for the |
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310 directed case). |
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311 |
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312 edge_attr : str or int, iterable, True, or None |
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313 A valid column name (str or int) or iterable of column names that are |
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314 used to retrieve items and add them to the graph as edge attributes. |
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315 If `True`, all of the remaining columns will be added. |
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316 If `None`, no edge attributes are added to the graph. |
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317 |
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318 create_using : NetworkX graph constructor, optional (default=nx.Graph) |
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319 Graph type to create. If graph instance, then cleared before populated. |
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320 |
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321 edge_key : str or None, optional (default=None) |
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322 A valid column name for the edge keys (for a MultiGraph). The values in |
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323 this column are used for the edge keys when adding edges if create_using |
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324 is a multigraph. |
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325 |
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326 See Also |
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327 -------- |
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328 to_pandas_edgelist |
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329 |
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330 Examples |
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331 -------- |
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332 Simple integer weights on edges: |
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333 |
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334 >>> import pandas as pd |
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335 >>> pd.options.display.max_columns = 20 |
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336 >>> import numpy as np |
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337 >>> rng = np.random.RandomState(seed=5) |
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338 >>> ints = rng.randint(1, 11, size=(3, 2)) |
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339 >>> a = ["A", "B", "C"] |
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340 >>> b = ["D", "A", "E"] |
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341 >>> df = pd.DataFrame(ints, columns=["weight", "cost"]) |
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342 >>> df[0] = a |
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343 >>> df["b"] = b |
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344 >>> df[["weight", "cost", 0, "b"]] |
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345 weight cost 0 b |
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346 0 4 7 A D |
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347 1 7 1 B A |
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348 2 10 9 C E |
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349 >>> G = nx.from_pandas_edgelist(df, 0, "b", ["weight", "cost"]) |
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350 >>> G["E"]["C"]["weight"] |
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351 10 |
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352 >>> G["E"]["C"]["cost"] |
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353 9 |
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354 >>> edges = pd.DataFrame( |
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355 ... { |
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356 ... "source": [0, 1, 2], |
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357 ... "target": [2, 2, 3], |
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358 ... "weight": [3, 4, 5], |
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359 ... "color": ["red", "blue", "blue"], |
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360 ... } |
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361 ... ) |
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362 >>> G = nx.from_pandas_edgelist(edges, edge_attr=True) |
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363 >>> G[0][2]["color"] |
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364 'red' |
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365 |
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366 Build multigraph with custom keys: |
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367 |
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368 >>> edges = pd.DataFrame( |
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369 ... { |
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370 ... "source": [0, 1, 2, 0], |
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371 ... "target": [2, 2, 3, 2], |
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372 ... "my_edge_key": ["A", "B", "C", "D"], |
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373 ... "weight": [3, 4, 5, 6], |
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374 ... "color": ["red", "blue", "blue", "blue"], |
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375 ... } |
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376 ... ) |
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377 >>> G = nx.from_pandas_edgelist( |
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378 ... edges, |
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379 ... edge_key="my_edge_key", |
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380 ... edge_attr=["weight", "color"], |
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381 ... create_using=nx.MultiGraph(), |
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382 ... ) |
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383 >>> G[0][2] |
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384 AtlasView({'A': {'weight': 3, 'color': 'red'}, 'D': {'weight': 6, 'color': 'blue'}}) |
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385 |
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386 |
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387 """ |
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388 g = nx.empty_graph(0, create_using) |
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389 |
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390 if edge_attr is None: |
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391 g.add_edges_from(zip(df[source], df[target])) |
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392 return g |
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393 |
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394 reserved_columns = [source, target] |
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395 |
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396 # Additional columns requested |
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397 attr_col_headings = [] |
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398 attribute_data = [] |
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399 if edge_attr is True: |
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400 attr_col_headings = [c for c in df.columns if c not in reserved_columns] |
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401 elif isinstance(edge_attr, (list, tuple)): |
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402 attr_col_headings = edge_attr |
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403 else: |
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404 attr_col_headings = [edge_attr] |
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405 if len(attr_col_headings) == 0: |
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406 raise nx.NetworkXError( |
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407 f"Invalid edge_attr argument: No columns found with name: {attr_col_headings}" |
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408 ) |
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409 |
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410 try: |
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411 attribute_data = zip(*[df[col] for col in attr_col_headings]) |
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412 except (KeyError, TypeError) as e: |
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413 msg = f"Invalid edge_attr argument: {edge_attr}" |
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414 raise nx.NetworkXError(msg) from e |
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415 |
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416 if g.is_multigraph(): |
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417 # => append the edge keys from the df to the bundled data |
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418 if edge_key is not None: |
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419 try: |
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420 multigraph_edge_keys = df[edge_key] |
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421 attribute_data = zip(attribute_data, multigraph_edge_keys) |
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422 except (KeyError, TypeError) as e: |
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423 msg = f"Invalid edge_key argument: {edge_key}" |
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424 raise nx.NetworkXError(msg) from e |
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425 |
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426 for s, t, attrs in zip(df[source], df[target], attribute_data): |
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427 if edge_key is not None: |
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428 attrs, multigraph_edge_key = attrs |
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429 key = g.add_edge(s, t, key=multigraph_edge_key) |
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430 else: |
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431 key = g.add_edge(s, t) |
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432 |
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433 g[s][t][key].update(zip(attr_col_headings, attrs)) |
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434 else: |
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435 for s, t, attrs in zip(df[source], df[target], attribute_data): |
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436 g.add_edge(s, t) |
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437 g[s][t].update(zip(attr_col_headings, attrs)) |
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438 |
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439 return g |
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440 |
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441 |
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442 def to_numpy_matrix( |
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443 G, |
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444 nodelist=None, |
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445 dtype=None, |
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446 order=None, |
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447 multigraph_weight=sum, |
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448 weight="weight", |
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449 nonedge=0.0, |
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450 ): |
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451 """Returns the graph adjacency matrix as a NumPy matrix. |
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452 |
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453 Parameters |
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454 ---------- |
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455 G : graph |
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456 The NetworkX graph used to construct the NumPy matrix. |
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457 |
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458 nodelist : list, optional |
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459 The rows and columns are ordered according to the nodes in `nodelist`. |
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460 If `nodelist` is None, then the ordering is produced by G.nodes(). |
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461 |
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462 dtype : NumPy data type, optional |
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463 A valid single NumPy data type used to initialize the array. |
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464 This must be a simple type such as int or numpy.float64 and |
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465 not a compound data type (see to_numpy_recarray) |
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466 If None, then the NumPy default is used. |
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467 |
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468 order : {'C', 'F'}, optional |
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469 Whether to store multidimensional data in C- or Fortran-contiguous |
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470 (row- or column-wise) order in memory. If None, then the NumPy default |
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471 is used. |
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472 |
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473 multigraph_weight : {sum, min, max}, optional |
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474 An operator that determines how weights in multigraphs are handled. |
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475 The default is to sum the weights of the multiple edges. |
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476 |
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477 weight : string or None optional (default = 'weight') |
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478 The edge attribute that holds the numerical value used for |
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479 the edge weight. If an edge does not have that attribute, then the |
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480 value 1 is used instead. |
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481 |
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482 nonedge : float (default = 0.0) |
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483 The matrix values corresponding to nonedges are typically set to zero. |
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484 However, this could be undesirable if there are matrix values |
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485 corresponding to actual edges that also have the value zero. If so, |
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486 one might prefer nonedges to have some other value, such as nan. |
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487 |
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488 Returns |
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489 ------- |
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490 M : NumPy matrix |
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491 Graph adjacency matrix |
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492 |
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493 See Also |
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494 -------- |
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495 to_numpy_recarray, from_numpy_matrix |
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496 |
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497 Notes |
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498 ----- |
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499 For directed graphs, entry i,j corresponds to an edge from i to j. |
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500 |
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501 The matrix entries are assigned to the weight edge attribute. When |
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502 an edge does not have a weight attribute, the value of the entry is set to |
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503 the number 1. For multiple (parallel) edges, the values of the entries |
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504 are determined by the `multigraph_weight` parameter. The default is to |
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505 sum the weight attributes for each of the parallel edges. |
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506 |
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507 When `nodelist` does not contain every node in `G`, the matrix is built |
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508 from the subgraph of `G` that is induced by the nodes in `nodelist`. |
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509 |
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510 The convention used for self-loop edges in graphs is to assign the |
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511 diagonal matrix entry value to the weight attribute of the edge |
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512 (or the number 1 if the edge has no weight attribute). If the |
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513 alternate convention of doubling the edge weight is desired the |
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514 resulting Numpy matrix can be modified as follows: |
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515 |
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516 >>> import numpy as np |
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517 >>> G = nx.Graph([(1, 1)]) |
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518 >>> A = nx.to_numpy_matrix(G) |
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519 >>> A |
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520 matrix([[1.]]) |
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521 >>> A[np.diag_indices_from(A)] *= 2 |
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522 >>> A |
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523 matrix([[2.]]) |
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524 |
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525 Examples |
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526 -------- |
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527 >>> G = nx.MultiDiGraph() |
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528 >>> G.add_edge(0, 1, weight=2) |
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529 0 |
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530 >>> G.add_edge(1, 0) |
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531 0 |
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532 >>> G.add_edge(2, 2, weight=3) |
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533 0 |
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534 >>> G.add_edge(2, 2) |
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535 1 |
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536 >>> nx.to_numpy_matrix(G, nodelist=[0, 1, 2]) |
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537 matrix([[0., 2., 0.], |
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538 [1., 0., 0.], |
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539 [0., 0., 4.]]) |
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540 |
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541 """ |
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542 import numpy as np |
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543 |
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544 A = to_numpy_array( |
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545 G, |
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546 nodelist=nodelist, |
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547 dtype=dtype, |
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548 order=order, |
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549 multigraph_weight=multigraph_weight, |
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550 weight=weight, |
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551 nonedge=nonedge, |
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552 ) |
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553 M = np.asmatrix(A, dtype=dtype) |
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554 return M |
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555 |
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556 |
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557 def from_numpy_matrix(A, parallel_edges=False, create_using=None): |
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558 """Returns a graph from numpy matrix. |
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559 |
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560 The numpy matrix is interpreted as an adjacency matrix for the graph. |
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561 |
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562 Parameters |
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563 ---------- |
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564 A : numpy matrix |
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565 An adjacency matrix representation of a graph |
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566 |
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567 parallel_edges : Boolean |
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568 If True, `create_using` is a multigraph, and `A` is an |
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569 integer matrix, then entry *(i, j)* in the matrix is interpreted as the |
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570 number of parallel edges joining vertices *i* and *j* in the graph. |
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571 If False, then the entries in the adjacency matrix are interpreted as |
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572 the weight of a single edge joining the vertices. |
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573 |
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574 create_using : NetworkX graph constructor, optional (default=nx.Graph) |
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575 Graph type to create. If graph instance, then cleared before populated. |
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576 |
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577 Notes |
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578 ----- |
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579 For directed graphs, explicitly mention create_using=nx.DiGraph, |
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580 and entry i,j of A corresponds to an edge from i to j. |
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581 |
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582 If `create_using` is :class:`networkx.MultiGraph` or |
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583 :class:`networkx.MultiDiGraph`, `parallel_edges` is True, and the |
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584 entries of `A` are of type :class:`int`, then this function returns a |
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585 multigraph (constructed from `create_using`) with parallel edges. |
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586 |
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587 If `create_using` indicates an undirected multigraph, then only the edges |
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588 indicated by the upper triangle of the matrix `A` will be added to the |
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589 graph. |
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590 |
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591 If the numpy matrix has a single data type for each matrix entry it |
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592 will be converted to an appropriate Python data type. |
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593 |
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594 If the numpy matrix has a user-specified compound data type the names |
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595 of the data fields will be used as attribute keys in the resulting |
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596 NetworkX graph. |
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597 |
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598 See Also |
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599 -------- |
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600 to_numpy_matrix, to_numpy_recarray |
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601 |
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602 Examples |
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603 -------- |
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604 Simple integer weights on edges: |
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605 |
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606 >>> import numpy as np |
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607 >>> A = np.array([[1, 1], [2, 1]]) |
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608 >>> G = nx.from_numpy_matrix(A) |
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609 |
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610 If `create_using` indicates a multigraph and the matrix has only integer |
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611 entries and `parallel_edges` is False, then the entries will be treated |
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612 as weights for edges joining the nodes (without creating parallel edges): |
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613 |
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614 >>> A = np.array([[1, 1], [1, 2]]) |
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615 >>> G = nx.from_numpy_matrix(A, create_using=nx.MultiGraph) |
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616 >>> G[1][1] |
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617 AtlasView({0: {'weight': 2}}) |
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618 |
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619 If `create_using` indicates a multigraph and the matrix has only integer |
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620 entries and `parallel_edges` is True, then the entries will be treated |
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621 as the number of parallel edges joining those two vertices: |
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622 |
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623 >>> A = np.array([[1, 1], [1, 2]]) |
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624 >>> temp = nx.MultiGraph() |
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625 >>> G = nx.from_numpy_matrix(A, parallel_edges=True, create_using=temp) |
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626 >>> G[1][1] |
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627 AtlasView({0: {'weight': 1}, 1: {'weight': 1}}) |
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628 |
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629 User defined compound data type on edges: |
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630 |
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631 >>> dt = [("weight", float), ("cost", int)] |
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632 >>> A = np.array([[(1.0, 2)]], dtype=dt) |
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633 >>> G = nx.from_numpy_matrix(A) |
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634 >>> list(G.edges()) |
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635 [(0, 0)] |
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636 >>> G[0][0]["cost"] |
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637 2 |
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638 >>> G[0][0]["weight"] |
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639 1.0 |
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640 |
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641 """ |
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642 # This should never fail if you have created a numpy matrix with numpy... |
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643 import numpy as np |
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644 |
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645 kind_to_python_type = { |
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646 "f": float, |
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647 "i": int, |
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648 "u": int, |
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649 "b": bool, |
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650 "c": complex, |
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651 "S": str, |
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652 "V": "void", |
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653 } |
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654 kind_to_python_type["U"] = str |
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655 G = nx.empty_graph(0, create_using) |
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656 n, m = A.shape |
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657 if n != m: |
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658 raise nx.NetworkXError(f"Adjacency matrix not square: nx,ny={A.shape}") |
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659 dt = A.dtype |
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660 try: |
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661 python_type = kind_to_python_type[dt.kind] |
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662 except Exception as e: |
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663 raise TypeError(f"Unknown numpy data type: {dt}") from e |
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664 |
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665 # Make sure we get even the isolated nodes of the graph. |
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666 G.add_nodes_from(range(n)) |
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667 # Get a list of all the entries in the matrix with nonzero entries. These |
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668 # coordinates become edges in the graph. (convert to int from np.int64) |
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669 edges = ((int(e[0]), int(e[1])) for e in zip(*np.asarray(A).nonzero())) |
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670 # handle numpy constructed data type |
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671 if python_type == "void": |
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672 # Sort the fields by their offset, then by dtype, then by name. |
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673 fields = sorted( |
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674 (offset, dtype, name) for name, (dtype, offset) in A.dtype.fields.items() |
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675 ) |
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676 triples = ( |
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677 ( |
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678 u, |
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679 v, |
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680 { |
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681 name: kind_to_python_type[dtype.kind](val) |
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682 for (_, dtype, name), val in zip(fields, A[u, v]) |
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683 }, |
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684 ) |
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685 for u, v in edges |
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686 ) |
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687 # If the entries in the adjacency matrix are integers, the graph is a |
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688 # multigraph, and parallel_edges is True, then create parallel edges, each |
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689 # with weight 1, for each entry in the adjacency matrix. Otherwise, create |
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690 # one edge for each positive entry in the adjacency matrix and set the |
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691 # weight of that edge to be the entry in the matrix. |
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692 elif python_type is int and G.is_multigraph() and parallel_edges: |
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693 chain = itertools.chain.from_iterable |
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694 # The following line is equivalent to: |
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695 # |
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696 # for (u, v) in edges: |
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697 # for d in range(A[u, v]): |
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698 # G.add_edge(u, v, weight=1) |
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699 # |
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700 triples = chain( |
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701 ((u, v, {"weight": 1}) for d in range(A[u, v])) for (u, v) in edges |
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702 ) |
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703 else: # basic data type |
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704 triples = ((u, v, dict(weight=python_type(A[u, v]))) for u, v in edges) |
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705 # If we are creating an undirected multigraph, only add the edges from the |
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706 # upper triangle of the matrix. Otherwise, add all the edges. This relies |
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707 # on the fact that the vertices created in the |
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708 # `_generated_weighted_edges()` function are actually the row/column |
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709 # indices for the matrix `A`. |
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710 # |
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711 # Without this check, we run into a problem where each edge is added twice |
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712 # when `G.add_edges_from()` is invoked below. |
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713 if G.is_multigraph() and not G.is_directed(): |
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714 triples = ((u, v, d) for u, v, d in triples if u <= v) |
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715 G.add_edges_from(triples) |
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716 return G |
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717 |
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718 |
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719 @not_implemented_for("multigraph") |
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720 def to_numpy_recarray(G, nodelist=None, dtype=None, order=None): |
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721 """Returns the graph adjacency matrix as a NumPy recarray. |
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722 |
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723 Parameters |
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724 ---------- |
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725 G : graph |
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726 The NetworkX graph used to construct the NumPy recarray. |
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727 |
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728 nodelist : list, optional |
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729 The rows and columns are ordered according to the nodes in `nodelist`. |
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730 If `nodelist` is None, then the ordering is produced by G.nodes(). |
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731 |
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732 dtype : NumPy data-type, optional |
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733 A valid NumPy named dtype used to initialize the NumPy recarray. |
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734 The data type names are assumed to be keys in the graph edge attribute |
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735 dictionary. |
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736 |
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737 order : {'C', 'F'}, optional |
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738 Whether to store multidimensional data in C- or Fortran-contiguous |
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739 (row- or column-wise) order in memory. If None, then the NumPy default |
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740 is used. |
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741 |
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742 Returns |
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743 ------- |
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744 M : NumPy recarray |
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745 The graph with specified edge data as a Numpy recarray |
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746 |
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747 Notes |
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748 ----- |
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749 When `nodelist` does not contain every node in `G`, the adjacency |
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750 matrix is built from the subgraph of `G` that is induced by the nodes in |
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751 `nodelist`. |
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752 |
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753 Examples |
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754 -------- |
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755 >>> G = nx.Graph() |
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756 >>> G.add_edge(1, 2, weight=7.0, cost=5) |
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757 >>> A = nx.to_numpy_recarray(G, dtype=[("weight", float), ("cost", int)]) |
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758 >>> print(A.weight) |
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759 [[0. 7.] |
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760 [7. 0.]] |
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761 >>> print(A.cost) |
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762 [[0 5] |
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763 [5 0]] |
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764 |
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765 """ |
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766 if dtype is None: |
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767 dtype = [("weight", float)] |
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768 import numpy as np |
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769 |
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770 if nodelist is None: |
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771 nodelist = list(G) |
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772 nodeset = set(nodelist) |
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773 if len(nodelist) != len(nodeset): |
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774 msg = "Ambiguous ordering: `nodelist` contained duplicates." |
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775 raise nx.NetworkXError(msg) |
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776 nlen = len(nodelist) |
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777 undirected = not G.is_directed() |
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778 index = dict(zip(nodelist, range(nlen))) |
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779 M = np.zeros((nlen, nlen), dtype=dtype, order=order) |
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780 |
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781 names = M.dtype.names |
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782 for u, v, attrs in G.edges(data=True): |
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783 if (u in nodeset) and (v in nodeset): |
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784 i, j = index[u], index[v] |
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785 values = tuple([attrs[n] for n in names]) |
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786 M[i, j] = values |
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787 if undirected: |
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788 M[j, i] = M[i, j] |
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789 |
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790 return M.view(np.recarray) |
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791 |
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792 |
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793 def to_scipy_sparse_matrix(G, nodelist=None, dtype=None, weight="weight", format="csr"): |
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794 """Returns the graph adjacency matrix as a SciPy sparse matrix. |
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795 |
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796 Parameters |
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797 ---------- |
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798 G : graph |
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799 The NetworkX graph used to construct the sparse matrix. |
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800 |
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801 nodelist : list, optional |
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802 The rows and columns are ordered according to the nodes in `nodelist`. |
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803 If `nodelist` is None, then the ordering is produced by G.nodes(). |
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804 |
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805 dtype : NumPy data-type, optional |
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806 A valid NumPy dtype used to initialize the array. If None, then the |
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807 NumPy default is used. |
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808 |
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809 weight : string or None optional (default='weight') |
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810 The edge attribute that holds the numerical value used for |
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811 the edge weight. If None then all edge weights are 1. |
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812 |
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813 format : str in {'bsr', 'csr', 'csc', 'coo', 'lil', 'dia', 'dok'} |
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814 The type of the matrix to be returned (default 'csr'). For |
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815 some algorithms different implementations of sparse matrices |
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816 can perform better. See [1]_ for details. |
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817 |
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818 Returns |
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819 ------- |
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820 M : SciPy sparse matrix |
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821 Graph adjacency matrix. |
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822 |
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823 Notes |
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824 ----- |
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825 For directed graphs, matrix entry i,j corresponds to an edge from i to j. |
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826 |
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827 The matrix entries are populated using the edge attribute held in |
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828 parameter weight. When an edge does not have that attribute, the |
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829 value of the entry is 1. |
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830 |
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831 For multiple edges the matrix values are the sums of the edge weights. |
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832 |
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833 When `nodelist` does not contain every node in `G`, the adjacency matrix |
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834 is built from the subgraph of `G` that is induced by the nodes in |
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835 `nodelist`. |
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836 |
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837 The convention used for self-loop edges in graphs is to assign the |
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838 diagonal matrix entry value to the weight attribute of the edge |
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839 (or the number 1 if the edge has no weight attribute). If the |
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840 alternate convention of doubling the edge weight is desired the |
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841 resulting Scipy sparse matrix can be modified as follows: |
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842 |
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843 >>> import scipy as sp |
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844 >>> G = nx.Graph([(1, 1)]) |
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845 >>> A = nx.to_scipy_sparse_matrix(G) |
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846 >>> print(A.todense()) |
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847 [[1]] |
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848 >>> A.setdiag(A.diagonal() * 2) |
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849 >>> print(A.todense()) |
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850 [[2]] |
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851 |
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852 Examples |
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853 -------- |
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854 >>> G = nx.MultiDiGraph() |
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855 >>> G.add_edge(0, 1, weight=2) |
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856 0 |
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857 >>> G.add_edge(1, 0) |
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858 0 |
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859 >>> G.add_edge(2, 2, weight=3) |
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860 0 |
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861 >>> G.add_edge(2, 2) |
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862 1 |
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863 >>> S = nx.to_scipy_sparse_matrix(G, nodelist=[0, 1, 2]) |
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864 >>> print(S.todense()) |
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865 [[0 2 0] |
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866 [1 0 0] |
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867 [0 0 4]] |
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868 |
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869 References |
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870 ---------- |
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871 .. [1] Scipy Dev. References, "Sparse Matrices", |
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872 https://docs.scipy.org/doc/scipy/reference/sparse.html |
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873 """ |
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874 from scipy import sparse |
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875 |
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876 if nodelist is None: |
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877 nodelist = list(G) |
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878 nlen = len(nodelist) |
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879 if nlen == 0: |
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880 raise nx.NetworkXError("Graph has no nodes or edges") |
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881 |
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882 if len(nodelist) != len(set(nodelist)): |
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883 msg = "Ambiguous ordering: `nodelist` contained duplicates." |
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884 raise nx.NetworkXError(msg) |
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885 |
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886 index = dict(zip(nodelist, range(nlen))) |
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887 coefficients = zip( |
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888 *( |
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889 (index[u], index[v], d.get(weight, 1)) |
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890 for u, v, d in G.edges(nodelist, data=True) |
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891 if u in index and v in index |
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892 ) |
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893 ) |
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894 try: |
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895 row, col, data = coefficients |
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896 except ValueError: |
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897 # there is no edge in the subgraph |
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898 row, col, data = [], [], [] |
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899 |
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900 if G.is_directed(): |
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901 M = sparse.coo_matrix((data, (row, col)), shape=(nlen, nlen), dtype=dtype) |
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902 else: |
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903 # symmetrize matrix |
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904 d = data + data |
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905 r = row + col |
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906 c = col + row |
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907 # selfloop entries get double counted when symmetrizing |
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908 # so we subtract the data on the diagonal |
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909 selfloops = list(nx.selfloop_edges(G.subgraph(nodelist), data=True)) |
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910 if selfloops: |
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911 diag_index, diag_data = zip( |
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912 *( |
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913 (index[u], -d.get(weight, 1)) |
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914 for u, v, d in selfloops |
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915 if u in index and v in index |
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916 ) |
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917 ) |
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918 d += diag_data |
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919 r += diag_index |
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920 c += diag_index |
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921 M = sparse.coo_matrix((d, (r, c)), shape=(nlen, nlen), dtype=dtype) |
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922 try: |
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923 return M.asformat(format) |
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924 # From Scipy 1.1.0, asformat will throw a ValueError instead of an |
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925 # AttributeError if the format if not recognized. |
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926 except (AttributeError, ValueError) as e: |
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927 raise nx.NetworkXError(f"Unknown sparse matrix format: {format}") from e |
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928 |
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929 |
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930 def _csr_gen_triples(A): |
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931 """Converts a SciPy sparse matrix in **Compressed Sparse Row** format to |
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932 an iterable of weighted edge triples. |
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933 |
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934 """ |
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935 nrows = A.shape[0] |
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936 data, indices, indptr = A.data, A.indices, A.indptr |
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937 for i in range(nrows): |
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938 for j in range(indptr[i], indptr[i + 1]): |
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939 yield i, indices[j], data[j] |
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940 |
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941 |
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942 def _csc_gen_triples(A): |
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943 """Converts a SciPy sparse matrix in **Compressed Sparse Column** format to |
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944 an iterable of weighted edge triples. |
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945 |
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946 """ |
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947 ncols = A.shape[1] |
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948 data, indices, indptr = A.data, A.indices, A.indptr |
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949 for i in range(ncols): |
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950 for j in range(indptr[i], indptr[i + 1]): |
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951 yield indices[j], i, data[j] |
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952 |
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953 |
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954 def _coo_gen_triples(A): |
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955 """Converts a SciPy sparse matrix in **Coordinate** format to an iterable |
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956 of weighted edge triples. |
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957 |
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958 """ |
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959 row, col, data = A.row, A.col, A.data |
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960 return zip(row, col, data) |
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961 |
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962 |
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963 def _dok_gen_triples(A): |
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964 """Converts a SciPy sparse matrix in **Dictionary of Keys** format to an |
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965 iterable of weighted edge triples. |
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966 |
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967 """ |
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968 for (r, c), v in A.items(): |
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969 yield r, c, v |
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970 |
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971 |
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972 def _generate_weighted_edges(A): |
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973 """Returns an iterable over (u, v, w) triples, where u and v are adjacent |
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974 vertices and w is the weight of the edge joining u and v. |
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975 |
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976 `A` is a SciPy sparse matrix (in any format). |
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977 |
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978 """ |
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979 if A.format == "csr": |
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980 return _csr_gen_triples(A) |
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981 if A.format == "csc": |
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982 return _csc_gen_triples(A) |
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983 if A.format == "dok": |
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984 return _dok_gen_triples(A) |
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985 # If A is in any other format (including COO), convert it to COO format. |
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986 return _coo_gen_triples(A.tocoo()) |
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987 |
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988 |
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989 def from_scipy_sparse_matrix( |
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990 A, parallel_edges=False, create_using=None, edge_attribute="weight" |
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991 ): |
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992 """Creates a new graph from an adjacency matrix given as a SciPy sparse |
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993 matrix. |
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994 |
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995 Parameters |
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996 ---------- |
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997 A: scipy sparse matrix |
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998 An adjacency matrix representation of a graph |
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999 |
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1000 parallel_edges : Boolean |
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1001 If this is True, `create_using` is a multigraph, and `A` is an |
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1002 integer matrix, then entry *(i, j)* in the matrix is interpreted as the |
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1003 number of parallel edges joining vertices *i* and *j* in the graph. |
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1004 If it is False, then the entries in the matrix are interpreted as |
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1005 the weight of a single edge joining the vertices. |
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1006 |
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1007 create_using : NetworkX graph constructor, optional (default=nx.Graph) |
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1008 Graph type to create. If graph instance, then cleared before populated. |
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1009 |
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1010 edge_attribute: string |
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1011 Name of edge attribute to store matrix numeric value. The data will |
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1012 have the same type as the matrix entry (int, float, (real,imag)). |
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1013 |
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1014 Notes |
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1015 ----- |
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1016 For directed graphs, explicitly mention create_using=nx.DiGraph, |
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1017 and entry i,j of A corresponds to an edge from i to j. |
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1018 |
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1019 If `create_using` is :class:`networkx.MultiGraph` or |
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1020 :class:`networkx.MultiDiGraph`, `parallel_edges` is True, and the |
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1021 entries of `A` are of type :class:`int`, then this function returns a |
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1022 multigraph (constructed from `create_using`) with parallel edges. |
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1023 In this case, `edge_attribute` will be ignored. |
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1024 |
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1025 If `create_using` indicates an undirected multigraph, then only the edges |
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1026 indicated by the upper triangle of the matrix `A` will be added to the |
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1027 graph. |
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1028 |
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1029 Examples |
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1030 -------- |
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1031 >>> import scipy as sp |
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1032 >>> A = sp.sparse.eye(2, 2, 1) |
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1033 >>> G = nx.from_scipy_sparse_matrix(A) |
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1034 |
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1035 If `create_using` indicates a multigraph and the matrix has only integer |
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1036 entries and `parallel_edges` is False, then the entries will be treated |
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1037 as weights for edges joining the nodes (without creating parallel edges): |
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1038 |
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1039 >>> A = sp.sparse.csr_matrix([[1, 1], [1, 2]]) |
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1040 >>> G = nx.from_scipy_sparse_matrix(A, create_using=nx.MultiGraph) |
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1041 >>> G[1][1] |
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1042 AtlasView({0: {'weight': 2}}) |
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1043 |
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1044 If `create_using` indicates a multigraph and the matrix has only integer |
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1045 entries and `parallel_edges` is True, then the entries will be treated |
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1046 as the number of parallel edges joining those two vertices: |
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1047 |
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1048 >>> A = sp.sparse.csr_matrix([[1, 1], [1, 2]]) |
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1049 >>> G = nx.from_scipy_sparse_matrix( |
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1050 ... A, parallel_edges=True, create_using=nx.MultiGraph |
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1051 ... ) |
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1052 >>> G[1][1] |
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1053 AtlasView({0: {'weight': 1}, 1: {'weight': 1}}) |
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1054 |
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1055 """ |
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1056 G = nx.empty_graph(0, create_using) |
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1057 n, m = A.shape |
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1058 if n != m: |
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1059 raise nx.NetworkXError(f"Adjacency matrix not square: nx,ny={A.shape}") |
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1060 # Make sure we get even the isolated nodes of the graph. |
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1061 G.add_nodes_from(range(n)) |
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1062 # Create an iterable over (u, v, w) triples and for each triple, add an |
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1063 # edge from u to v with weight w. |
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1064 triples = _generate_weighted_edges(A) |
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1065 # If the entries in the adjacency matrix are integers, the graph is a |
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1066 # multigraph, and parallel_edges is True, then create parallel edges, each |
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1067 # with weight 1, for each entry in the adjacency matrix. Otherwise, create |
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1068 # one edge for each positive entry in the adjacency matrix and set the |
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1069 # weight of that edge to be the entry in the matrix. |
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1070 if A.dtype.kind in ("i", "u") and G.is_multigraph() and parallel_edges: |
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1071 chain = itertools.chain.from_iterable |
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1072 # The following line is equivalent to: |
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1073 # |
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1074 # for (u, v) in edges: |
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1075 # for d in range(A[u, v]): |
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1076 # G.add_edge(u, v, weight=1) |
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1077 # |
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1078 triples = chain(((u, v, 1) for d in range(w)) for (u, v, w) in triples) |
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1079 # If we are creating an undirected multigraph, only add the edges from the |
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1080 # upper triangle of the matrix. Otherwise, add all the edges. This relies |
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1081 # on the fact that the vertices created in the |
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1082 # `_generated_weighted_edges()` function are actually the row/column |
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1083 # indices for the matrix `A`. |
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1084 # |
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1085 # Without this check, we run into a problem where each edge is added twice |
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1086 # when `G.add_weighted_edges_from()` is invoked below. |
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1087 if G.is_multigraph() and not G.is_directed(): |
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1088 triples = ((u, v, d) for u, v, d in triples if u <= v) |
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1089 G.add_weighted_edges_from(triples, weight=edge_attribute) |
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1090 return G |
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1091 |
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1092 |
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1093 def to_numpy_array( |
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1094 G, |
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1095 nodelist=None, |
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1096 dtype=None, |
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1097 order=None, |
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1098 multigraph_weight=sum, |
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1099 weight="weight", |
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1100 nonedge=0.0, |
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1101 ): |
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1102 """Returns the graph adjacency matrix as a NumPy array. |
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1103 |
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1104 Parameters |
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1105 ---------- |
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1106 G : graph |
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1107 The NetworkX graph used to construct the NumPy array. |
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1108 |
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1109 nodelist : list, optional |
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1110 The rows and columns are ordered according to the nodes in `nodelist`. |
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1111 If `nodelist` is None, then the ordering is produced by G.nodes(). |
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1112 |
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1113 dtype : NumPy data type, optional |
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1114 A valid single NumPy data type used to initialize the array. |
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1115 This must be a simple type such as int or numpy.float64 and |
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1116 not a compound data type (see to_numpy_recarray) |
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1117 If None, then the NumPy default is used. |
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1118 |
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1119 order : {'C', 'F'}, optional |
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1120 Whether to store multidimensional data in C- or Fortran-contiguous |
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1121 (row- or column-wise) order in memory. If None, then the NumPy default |
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1122 is used. |
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1123 |
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1124 multigraph_weight : {sum, min, max}, optional |
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1125 An operator that determines how weights in multigraphs are handled. |
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1126 The default is to sum the weights of the multiple edges. |
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1127 |
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1128 weight : string or None optional (default = 'weight') |
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1129 The edge attribute that holds the numerical value used for |
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1130 the edge weight. If an edge does not have that attribute, then the |
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1131 value 1 is used instead. |
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1132 |
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1133 nonedge : float (default = 0.0) |
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1134 The array values corresponding to nonedges are typically set to zero. |
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1135 However, this could be undesirable if there are array values |
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1136 corresponding to actual edges that also have the value zero. If so, |
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1137 one might prefer nonedges to have some other value, such as nan. |
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1138 |
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1139 Returns |
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1140 ------- |
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1141 A : NumPy ndarray |
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1142 Graph adjacency matrix |
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1143 |
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1144 See Also |
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1145 -------- |
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1146 from_numpy_array |
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1147 |
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1148 Notes |
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1149 ----- |
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1150 For directed graphs, entry i,j corresponds to an edge from i to j. |
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1151 |
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1152 Entries in the adjacency matrix are assigned to the weight edge attribute. |
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1153 When an edge does not have a weight attribute, the value of the entry is |
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1154 set to the number 1. For multiple (parallel) edges, the values of the |
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1155 entries are determined by the `multigraph_weight` parameter. The default is |
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1156 to sum the weight attributes for each of the parallel edges. |
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1157 |
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1158 When `nodelist` does not contain every node in `G`, the adjacency matrix is |
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1159 built from the subgraph of `G` that is induced by the nodes in `nodelist`. |
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1160 |
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1161 The convention used for self-loop edges in graphs is to assign the |
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1162 diagonal array entry value to the weight attribute of the edge |
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1163 (or the number 1 if the edge has no weight attribute). If the |
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1164 alternate convention of doubling the edge weight is desired the |
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1165 resulting NumPy array can be modified as follows: |
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1166 |
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1167 >>> import numpy as np |
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1168 >>> G = nx.Graph([(1, 1)]) |
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1169 >>> A = nx.to_numpy_array(G) |
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1170 >>> A |
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1171 array([[1.]]) |
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1172 >>> A[np.diag_indices_from(A)] *= 2 |
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1173 >>> A |
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1174 array([[2.]]) |
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1175 |
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1176 Examples |
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1177 -------- |
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1178 >>> G = nx.MultiDiGraph() |
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1179 >>> G.add_edge(0, 1, weight=2) |
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1180 0 |
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1181 >>> G.add_edge(1, 0) |
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1182 0 |
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1183 >>> G.add_edge(2, 2, weight=3) |
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1184 0 |
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1185 >>> G.add_edge(2, 2) |
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1186 1 |
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1187 >>> nx.to_numpy_array(G, nodelist=[0, 1, 2]) |
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1188 array([[0., 2., 0.], |
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1189 [1., 0., 0.], |
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1190 [0., 0., 4.]]) |
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1191 |
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1192 """ |
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1193 import numpy as np |
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1194 |
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1195 if nodelist is None: |
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1196 nodelist = list(G) |
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1197 nodeset = set(nodelist) |
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1198 if len(nodelist) != len(nodeset): |
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1199 msg = "Ambiguous ordering: `nodelist` contained duplicates." |
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1200 raise nx.NetworkXError(msg) |
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1201 |
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1202 nlen = len(nodelist) |
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1203 undirected = not G.is_directed() |
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1204 index = dict(zip(nodelist, range(nlen))) |
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1205 |
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1206 # Initially, we start with an array of nans. Then we populate the array |
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1207 # using data from the graph. Afterwards, any leftover nans will be |
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1208 # converted to the value of `nonedge`. Note, we use nans initially, |
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1209 # instead of zero, for two reasons: |
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1210 # |
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1211 # 1) It can be important to distinguish a real edge with the value 0 |
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1212 # from a nonedge with the value 0. |
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1213 # |
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1214 # 2) When working with multi(di)graphs, we must combine the values of all |
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1215 # edges between any two nodes in some manner. This often takes the |
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1216 # form of a sum, min, or max. Using the value 0 for a nonedge would |
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1217 # have undesirable effects with min and max, but using nanmin and |
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1218 # nanmax with initially nan values is not problematic at all. |
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1219 # |
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1220 # That said, there are still some drawbacks to this approach. Namely, if |
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1221 # a real edge is nan, then that value is a) not distinguishable from |
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1222 # nonedges and b) is ignored by the default combinator (nansum, nanmin, |
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1223 # nanmax) functions used for multi(di)graphs. If this becomes an issue, |
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1224 # an alternative approach is to use masked arrays. Initially, every |
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1225 # element is masked and set to some `initial` value. As we populate the |
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1226 # graph, elements are unmasked (automatically) when we combine the initial |
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1227 # value with the values given by real edges. At the end, we convert all |
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1228 # masked values to `nonedge`. Using masked arrays fully addresses reason 1, |
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1229 # but for reason 2, we would still have the issue with min and max if the |
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1230 # initial values were 0.0. Note: an initial value of +inf is appropriate |
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1231 # for min, while an initial value of -inf is appropriate for max. When |
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1232 # working with sum, an initial value of zero is appropriate. Ideally then, |
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1233 # we'd want to allow users to specify both a value for nonedges and also |
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1234 # an initial value. For multi(di)graphs, the choice of the initial value |
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1235 # will, in general, depend on the combinator function---sensible defaults |
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1236 # can be provided. |
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1237 |
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1238 if G.is_multigraph(): |
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1239 # Handle MultiGraphs and MultiDiGraphs |
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1240 A = np.full((nlen, nlen), np.nan, order=order) |
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1241 # use numpy nan-aware operations |
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1242 operator = {sum: np.nansum, min: np.nanmin, max: np.nanmax} |
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1243 try: |
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1244 op = operator[multigraph_weight] |
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1245 except Exception as e: |
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1246 raise ValueError("multigraph_weight must be sum, min, or max") from e |
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1247 |
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1248 for u, v, attrs in G.edges(data=True): |
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1249 if (u in nodeset) and (v in nodeset): |
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1250 i, j = index[u], index[v] |
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1251 e_weight = attrs.get(weight, 1) |
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1252 A[i, j] = op([e_weight, A[i, j]]) |
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1253 if undirected: |
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1254 A[j, i] = A[i, j] |
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1255 else: |
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1256 # Graph or DiGraph, this is much faster than above |
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1257 A = np.full((nlen, nlen), np.nan, order=order) |
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1258 for u, nbrdict in G.adjacency(): |
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1259 for v, d in nbrdict.items(): |
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1260 try: |
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1261 A[index[u], index[v]] = d.get(weight, 1) |
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1262 except KeyError: |
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1263 # This occurs when there are fewer desired nodes than |
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1264 # there are nodes in the graph: len(nodelist) < len(G) |
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1265 pass |
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1266 |
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1267 A[np.isnan(A)] = nonedge |
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1268 A = np.asarray(A, dtype=dtype) |
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1269 return A |
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1270 |
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1271 |
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1272 def from_numpy_array(A, parallel_edges=False, create_using=None): |
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1273 """Returns a graph from NumPy array. |
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1274 |
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1275 The NumPy array is interpreted as an adjacency matrix for the graph. |
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1276 |
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1277 Parameters |
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1278 ---------- |
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1279 A : NumPy ndarray |
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1280 An adjacency matrix representation of a graph |
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1281 |
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1282 parallel_edges : Boolean |
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1283 If this is True, `create_using` is a multigraph, and `A` is an |
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1284 integer array, then entry *(i, j)* in the array is interpreted as the |
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1285 number of parallel edges joining vertices *i* and *j* in the graph. |
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1286 If it is False, then the entries in the array are interpreted as |
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1287 the weight of a single edge joining the vertices. |
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1288 |
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1289 create_using : NetworkX graph constructor, optional (default=nx.Graph) |
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1290 Graph type to create. If graph instance, then cleared before populated. |
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1291 |
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1292 Notes |
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1293 ----- |
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1294 For directed graphs, explicitly mention create_using=nx.DiGraph, |
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1295 and entry i,j of A corresponds to an edge from i to j. |
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1296 |
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1297 If `create_using` is :class:`networkx.MultiGraph` or |
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1298 :class:`networkx.MultiDiGraph`, `parallel_edges` is True, and the |
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1299 entries of `A` are of type :class:`int`, then this function returns a |
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1300 multigraph (of the same type as `create_using`) with parallel edges. |
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1301 |
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1302 If `create_using` indicates an undirected multigraph, then only the edges |
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1303 indicated by the upper triangle of the array `A` will be added to the |
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1304 graph. |
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1305 |
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1306 If the NumPy array has a single data type for each array entry it |
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1307 will be converted to an appropriate Python data type. |
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1308 |
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1309 If the NumPy array has a user-specified compound data type the names |
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1310 of the data fields will be used as attribute keys in the resulting |
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1311 NetworkX graph. |
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1312 |
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1313 See Also |
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1314 -------- |
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1315 to_numpy_array |
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1316 |
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1317 Examples |
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1318 -------- |
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1319 Simple integer weights on edges: |
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1320 |
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1321 >>> import numpy as np |
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1322 >>> A = np.array([[1, 1], [2, 1]]) |
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1323 >>> G = nx.from_numpy_array(A) |
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1324 >>> G.edges(data=True) |
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1325 EdgeDataView([(0, 0, {'weight': 1}), (0, 1, {'weight': 2}), \ |
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1326 (1, 1, {'weight': 1})]) |
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1327 |
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1328 If `create_using` indicates a multigraph and the array has only integer |
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1329 entries and `parallel_edges` is False, then the entries will be treated |
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1330 as weights for edges joining the nodes (without creating parallel edges): |
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1331 |
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1332 >>> A = np.array([[1, 1], [1, 2]]) |
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1333 >>> G = nx.from_numpy_array(A, create_using=nx.MultiGraph) |
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1334 >>> G[1][1] |
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1335 AtlasView({0: {'weight': 2}}) |
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1336 |
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1337 If `create_using` indicates a multigraph and the array has only integer |
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1338 entries and `parallel_edges` is True, then the entries will be treated |
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1339 as the number of parallel edges joining those two vertices: |
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1340 |
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1341 >>> A = np.array([[1, 1], [1, 2]]) |
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1342 >>> temp = nx.MultiGraph() |
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1343 >>> G = nx.from_numpy_array(A, parallel_edges=True, create_using=temp) |
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1344 >>> G[1][1] |
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1345 AtlasView({0: {'weight': 1}, 1: {'weight': 1}}) |
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1346 |
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1347 User defined compound data type on edges: |
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1348 |
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1349 >>> dt = [("weight", float), ("cost", int)] |
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1350 >>> A = np.array([[(1.0, 2)]], dtype=dt) |
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1351 >>> G = nx.from_numpy_array(A) |
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1352 >>> G.edges() |
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1353 EdgeView([(0, 0)]) |
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1354 >>> G[0][0]["cost"] |
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1355 2 |
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1356 >>> G[0][0]["weight"] |
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1357 1.0 |
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1358 |
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1359 """ |
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1360 return from_numpy_matrix( |
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1361 A, parallel_edges=parallel_edges, create_using=create_using |
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1362 ) |