Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/sitepackages/networkx/algorithms/bipartite/generators.py @ 0:4f3585e2f14b draft default tip
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author  shellac 

date  Mon, 22 Mar 2021 18:12:50 +0000 
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1 """ 
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2 Generators and functions for bipartite graphs. 
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3 """ 
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4 import math 
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5 import numbers 
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6 from functools import reduce 
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7 import networkx as nx 
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8 from networkx.utils import nodes_or_number, py_random_state 
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9 
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10 __all__ = [ 
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11 "configuration_model", 
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12 "havel_hakimi_graph", 
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13 "reverse_havel_hakimi_graph", 
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14 "alternating_havel_hakimi_graph", 
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15 "preferential_attachment_graph", 
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16 "random_graph", 
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17 "gnmk_random_graph", 
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18 "complete_bipartite_graph", 
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19 ] 
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20 
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21 
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22 @nodes_or_number([0, 1]) 
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23 def complete_bipartite_graph(n1, n2, create_using=None): 
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24 """Returns the complete bipartite graph `K_{n_1,n_2}`. 
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25 
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26 The graph is composed of two partitions with nodes 0 to (n1  1) 
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27 in the first and nodes n1 to (n1 + n2  1) in the second. 
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28 Each node in the first is connected to each node in the second. 
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29 
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30 Parameters 
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31  
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32 n1 : integer 
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33 Number of nodes for node set A. 
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34 n2 : integer 
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35 Number of nodes for node set B. 
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36 create_using : NetworkX graph instance, optional 
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37 Return graph of this type. 
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38 
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39 Notes 
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40  
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41 Node labels are the integers 0 to `n_1 + n_2  1`. 
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42 
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43 The nodes are assigned the attribute 'bipartite' with the value 0 or 1 
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44 to indicate which bipartite set the node belongs to. 
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45 
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46 This function is not imported in the main namespace. 
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47 To use it use nx.bipartite.complete_bipartite_graph 
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48 """ 
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49 G = nx.empty_graph(0, create_using) 
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50 if G.is_directed(): 
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51 raise nx.NetworkXError("Directed Graph not supported") 
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52 
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53 n1, top = n1 
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54 n2, bottom = n2 
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55 if isinstance(n2, numbers.Integral): 
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56 bottom = [n1 + i for i in bottom] 
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57 G.add_nodes_from(top, bipartite=0) 
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58 G.add_nodes_from(bottom, bipartite=1) 
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59 G.add_edges_from((u, v) for u in top for v in bottom) 
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60 G.graph["name"] = f"complete_bipartite_graph({n1},{n2})" 
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61 return G 
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62 
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63 
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64 @py_random_state(3) 
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65 def configuration_model(aseq, bseq, create_using=None, seed=None): 
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66 """Returns a random bipartite graph from two given degree sequences. 
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67 
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68 Parameters 
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69  
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70 aseq : list 
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71 Degree sequence for node set A. 
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72 bseq : list 
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73 Degree sequence for node set B. 
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74 create_using : NetworkX graph instance, optional 
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75 Return graph of this type. 
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76 seed : integer, random_state, or None (default) 
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77 Indicator of random number generation state. 
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78 See :ref:`Randomness<randomness>`. 
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79 
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80 The graph is composed of two partitions. Set A has nodes 0 to 
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81 (len(aseq)  1) and set B has nodes len(aseq) to (len(bseq)  1). 
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82 Nodes from set A are connected to nodes in set B by choosing 
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83 randomly from the possible free stubs, one in A and one in B. 
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84 
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85 Notes 
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86  
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87 The sum of the two sequences must be equal: sum(aseq)=sum(bseq) 
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88 If no graph type is specified use MultiGraph with parallel edges. 
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89 If you want a graph with no parallel edges use create_using=Graph() 
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90 but then the resulting degree sequences might not be exact. 
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91 
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92 The nodes are assigned the attribute 'bipartite' with the value 0 or 1 
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93 to indicate which bipartite set the node belongs to. 
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94 
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95 This function is not imported in the main namespace. 
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96 To use it use nx.bipartite.configuration_model 
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97 """ 
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98 G = nx.empty_graph(0, create_using, default=nx.MultiGraph) 
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99 if G.is_directed(): 
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100 raise nx.NetworkXError("Directed Graph not supported") 
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101 
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102 # length and sum of each sequence 
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103 lena = len(aseq) 
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104 lenb = len(bseq) 
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105 suma = sum(aseq) 
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106 sumb = sum(bseq) 
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107 
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108 if not suma == sumb: 
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109 raise nx.NetworkXError( 
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110 f"invalid degree sequences, sum(aseq)!=sum(bseq),{suma},{sumb}" 
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111 ) 
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112 
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113 G = _add_nodes_with_bipartite_label(G, lena, lenb) 
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114 
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115 if len(aseq) == 0 or max(aseq) == 0: 
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116 return G # done if no edges 
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117 
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118 # build lists of degreerepeated vertex numbers 
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119 stubs = [] 
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120 stubs.extend([[v] * aseq[v] for v in range(0, lena)]) 
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121 astubs = [] 
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122 astubs = [x for subseq in stubs for x in subseq] 
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123 
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124 stubs = [] 
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125 stubs.extend([[v] * bseq[v  lena] for v in range(lena, lena + lenb)]) 
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126 bstubs = [] 
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127 bstubs = [x for subseq in stubs for x in subseq] 
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128 
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129 # shuffle lists 
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130 seed.shuffle(astubs) 
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131 seed.shuffle(bstubs) 
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132 
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133 G.add_edges_from([[astubs[i], bstubs[i]] for i in range(suma)]) 
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134 
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135 G.name = "bipartite_configuration_model" 
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136 return G 
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137 
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138 
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139 def havel_hakimi_graph(aseq, bseq, create_using=None): 
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140 """Returns a bipartite graph from two given degree sequences using a 
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141 HavelHakimi style construction. 
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142 
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143 The graph is composed of two partitions. Set A has nodes 0 to 
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144 (len(aseq)  1) and set B has nodes len(aseq) to (len(bseq)  1). 
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145 Nodes from the set A are connected to nodes in the set B by 
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146 connecting the highest degree nodes in set A to the highest degree 
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147 nodes in set B until all stubs are connected. 
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148 
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149 Parameters 
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150  
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151 aseq : list 
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152 Degree sequence for node set A. 
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153 bseq : list 
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154 Degree sequence for node set B. 
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155 create_using : NetworkX graph instance, optional 
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156 Return graph of this type. 
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157 
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158 Notes 
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159  
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160 The sum of the two sequences must be equal: sum(aseq)=sum(bseq) 
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161 If no graph type is specified use MultiGraph with parallel edges. 
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162 If you want a graph with no parallel edges use create_using=Graph() 
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163 but then the resulting degree sequences might not be exact. 
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164 
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165 The nodes are assigned the attribute 'bipartite' with the value 0 or 1 
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166 to indicate which bipartite set the node belongs to. 
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167 
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168 This function is not imported in the main namespace. 
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169 To use it use nx.bipartite.havel_hakimi_graph 
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170 """ 
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171 G = nx.empty_graph(0, create_using, default=nx.MultiGraph) 
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172 if G.is_directed(): 
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173 raise nx.NetworkXError("Directed Graph not supported") 
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174 
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175 # length of the each sequence 
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176 naseq = len(aseq) 
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177 nbseq = len(bseq) 
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178 
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179 suma = sum(aseq) 
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180 sumb = sum(bseq) 
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181 
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182 if not suma == sumb: 
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183 raise nx.NetworkXError( 
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184 f"invalid degree sequences, sum(aseq)!=sum(bseq),{suma},{sumb}" 
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185 ) 
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186 
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187 G = _add_nodes_with_bipartite_label(G, naseq, nbseq) 
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188 
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189 if len(aseq) == 0 or max(aseq) == 0: 
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190 return G # done if no edges 
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191 
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192 # build list of degreerepeated vertex numbers 
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193 astubs = [[aseq[v], v] for v in range(0, naseq)] 
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194 bstubs = [[bseq[v  naseq], v] for v in range(naseq, naseq + nbseq)] 
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195 astubs.sort() 
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196 while astubs: 
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197 (degree, u) = astubs.pop() # take of largest degree node in the a set 
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198 if degree == 0: 
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199 break # done, all are zero 
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200 # connect the source to largest degree nodes in the b set 
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201 bstubs.sort() 
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202 for target in bstubs[degree:]: 
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203 v = target[1] 
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204 G.add_edge(u, v) 
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205 target[0] = 1 # note this updates bstubs too. 
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206 if target[0] == 0: 
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207 bstubs.remove(target) 
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208 
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209 G.name = "bipartite_havel_hakimi_graph" 
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210 return G 
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211 
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212 
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213 def reverse_havel_hakimi_graph(aseq, bseq, create_using=None): 
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214 """Returns a bipartite graph from two given degree sequences using a 
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215 HavelHakimi style construction. 
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216 
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217 The graph is composed of two partitions. Set A has nodes 0 to 
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218 (len(aseq)  1) and set B has nodes len(aseq) to (len(bseq)  1). 
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219 Nodes from set A are connected to nodes in the set B by connecting 
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220 the highest degree nodes in set A to the lowest degree nodes in 
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221 set B until all stubs are connected. 
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222 
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223 Parameters 
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224  
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225 aseq : list 
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226 Degree sequence for node set A. 
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227 bseq : list 
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228 Degree sequence for node set B. 
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229 create_using : NetworkX graph instance, optional 
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230 Return graph of this type. 
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231 
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232 Notes 
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233  
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234 The sum of the two sequences must be equal: sum(aseq)=sum(bseq) 
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235 If no graph type is specified use MultiGraph with parallel edges. 
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236 If you want a graph with no parallel edges use create_using=Graph() 
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237 but then the resulting degree sequences might not be exact. 
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238 
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239 The nodes are assigned the attribute 'bipartite' with the value 0 or 1 
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240 to indicate which bipartite set the node belongs to. 
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241 
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242 This function is not imported in the main namespace. 
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243 To use it use nx.bipartite.reverse_havel_hakimi_graph 
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244 """ 
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245 G = nx.empty_graph(0, create_using, default=nx.MultiGraph) 
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246 if G.is_directed(): 
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247 raise nx.NetworkXError("Directed Graph not supported") 
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248 
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249 # length of the each sequence 
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250 lena = len(aseq) 
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251 lenb = len(bseq) 
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252 suma = sum(aseq) 
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253 sumb = sum(bseq) 
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254 
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255 if not suma == sumb: 
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256 raise nx.NetworkXError( 
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257 f"invalid degree sequences, sum(aseq)!=sum(bseq),{suma},{sumb}" 
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258 ) 
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259 
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260 G = _add_nodes_with_bipartite_label(G, lena, lenb) 
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261 
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262 if len(aseq) == 0 or max(aseq) == 0: 
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263 return G # done if no edges 
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264 
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265 # build list of degreerepeated vertex numbers 
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266 astubs = [[aseq[v], v] for v in range(0, lena)] 
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267 bstubs = [[bseq[v  lena], v] for v in range(lena, lena + lenb)] 
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268 astubs.sort() 
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269 bstubs.sort() 
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270 while astubs: 
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271 (degree, u) = astubs.pop() # take of largest degree node in the a set 
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272 if degree == 0: 
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273 break # done, all are zero 
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274 # connect the source to the smallest degree nodes in the b set 
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275 for target in bstubs[0:degree]: 
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276 v = target[1] 
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277 G.add_edge(u, v) 
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278 target[0] = 1 # note this updates bstubs too. 
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279 if target[0] == 0: 
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280 bstubs.remove(target) 
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281 
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282 G.name = "bipartite_reverse_havel_hakimi_graph" 
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283 return G 
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284 
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285 
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286 def alternating_havel_hakimi_graph(aseq, bseq, create_using=None): 
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287 """Returns a bipartite graph from two given degree sequences using 
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288 an alternating HavelHakimi style construction. 
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289 
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290 The graph is composed of two partitions. Set A has nodes 0 to 
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291 (len(aseq)  1) and set B has nodes len(aseq) to (len(bseq)  1). 
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292 Nodes from the set A are connected to nodes in the set B by 
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293 connecting the highest degree nodes in set A to alternatively the 
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294 highest and the lowest degree nodes in set B until all stubs are 
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295 connected. 
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296 
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297 Parameters 
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298  
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299 aseq : list 
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300 Degree sequence for node set A. 
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301 bseq : list 
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302 Degree sequence for node set B. 
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303 create_using : NetworkX graph instance, optional 
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304 Return graph of this type. 
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305 
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306 Notes 
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307  
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308 The sum of the two sequences must be equal: sum(aseq)=sum(bseq) 
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309 If no graph type is specified use MultiGraph with parallel edges. 
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310 If you want a graph with no parallel edges use create_using=Graph() 
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311 but then the resulting degree sequences might not be exact. 
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312 
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313 The nodes are assigned the attribute 'bipartite' with the value 0 or 1 
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314 to indicate which bipartite set the node belongs to. 
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315 
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316 This function is not imported in the main namespace. 
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317 To use it use nx.bipartite.alternating_havel_hakimi_graph 
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318 """ 
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319 G = nx.empty_graph(0, create_using, default=nx.MultiGraph) 
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320 if G.is_directed(): 
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321 raise nx.NetworkXError("Directed Graph not supported") 
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322 
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323 # length of the each sequence 
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324 naseq = len(aseq) 
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325 nbseq = len(bseq) 
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326 suma = sum(aseq) 
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327 sumb = sum(bseq) 
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328 
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329 if not suma == sumb: 
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330 raise nx.NetworkXError( 
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331 f"invalid degree sequences, sum(aseq)!=sum(bseq),{suma},{sumb}" 
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332 ) 
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333 
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334 G = _add_nodes_with_bipartite_label(G, naseq, nbseq) 
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335 
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336 if len(aseq) == 0 or max(aseq) == 0: 
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337 return G # done if no edges 
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338 # build list of degreerepeated vertex numbers 
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339 astubs = [[aseq[v], v] for v in range(0, naseq)] 
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340 bstubs = [[bseq[v  naseq], v] for v in range(naseq, naseq + nbseq)] 
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341 while astubs: 
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342 astubs.sort() 
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343 (degree, u) = astubs.pop() # take of largest degree node in the a set 
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344 if degree == 0: 
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345 break # done, all are zero 
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346 bstubs.sort() 
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347 small = bstubs[0 : degree // 2] # add these low degree targets 
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348 large = bstubs[(degree + degree // 2) :] # now high degree targets 
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349 stubs = [x for z in zip(large, small) for x in z] # combine, sorry 
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350 if len(stubs) < len(small) + len(large): # check for zip truncation 
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351 stubs.append(large.pop()) 
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352 for target in stubs: 
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353 v = target[1] 
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354 G.add_edge(u, v) 
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355 target[0] = 1 # note this updates bstubs too. 
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356 if target[0] == 0: 
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357 bstubs.remove(target) 
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358 
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359 G.name = "bipartite_alternating_havel_hakimi_graph" 
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360 return G 
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361 
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362 
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363 @py_random_state(3) 
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364 def preferential_attachment_graph(aseq, p, create_using=None, seed=None): 
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365 """Create a bipartite graph with a preferential attachment model from 
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366 a given single degree sequence. 
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367 
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368 The graph is composed of two partitions. Set A has nodes 0 to 
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369 (len(aseq)  1) and set B has nodes starting with node len(aseq). 
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370 The number of nodes in set B is random. 
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371 
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372 Parameters 
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373  
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374 aseq : list 
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375 Degree sequence for node set A. 
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376 p : float 
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377 Probability that a new bottom node is added. 
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378 create_using : NetworkX graph instance, optional 
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379 Return graph of this type. 
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380 seed : integer, random_state, or None (default) 
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381 Indicator of random number generation state. 
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382 See :ref:`Randomness<randomness>`. 
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383 
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384 References 
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385  
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386 .. [1] Guillaume, J.L. and Latapy, M., 
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387 Bipartite graphs as models of complex networks. 
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388 Physica A: Statistical Mechanics and its Applications, 
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389 2006, 371(2), pp.795813. 
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390 .. [2] JeanLoup Guillaume and Matthieu Latapy, 
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391 Bipartite structure of all complex networks, 
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392 Inf. Process. Lett. 90, 2004, pg. 215221 
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393 https://doi.org/10.1016/j.ipl.2004.03.007 
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394 
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395 Notes 
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396  
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397 The nodes are assigned the attribute 'bipartite' with the value 0 or 1 
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398 to indicate which bipartite set the node belongs to. 
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399 
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400 This function is not imported in the main namespace. 
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401 To use it use nx.bipartite.preferential_attachment_graph 
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402 """ 
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403 G = nx.empty_graph(0, create_using, default=nx.MultiGraph) 
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404 if G.is_directed(): 
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405 raise nx.NetworkXError("Directed Graph not supported") 
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406 
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407 if p > 1: 
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408 raise nx.NetworkXError(f"probability {p} > 1") 
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409 
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410 naseq = len(aseq) 
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411 G = _add_nodes_with_bipartite_label(G, naseq, 0) 
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412 vv = [[v] * aseq[v] for v in range(0, naseq)] 
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413 while vv: 
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414 while vv[0]: 
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415 source = vv[0][0] 
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416 vv[0].remove(source) 
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417 if seed.random() < p or len(G) == naseq: 
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418 target = len(G) 
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419 G.add_node(target, bipartite=1) 
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420 G.add_edge(source, target) 
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421 else: 
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422 bb = [[b] * G.degree(b) for b in range(naseq, len(G))] 
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423 # flatten the list of lists into a list. 
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424 bbstubs = reduce(lambda x, y: x + y, bb) 
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425 # choose preferentially a bottom node. 
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426 target = seed.choice(bbstubs) 
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427 G.add_node(target, bipartite=1) 
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428 G.add_edge(source, target) 
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429 vv.remove(vv[0]) 
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430 G.name = "bipartite_preferential_attachment_model" 
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431 return G 
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432 
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433 
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434 @py_random_state(3) 
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435 def random_graph(n, m, p, seed=None, directed=False): 
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436 """Returns a bipartite random graph. 
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437 
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438 This is a bipartite version of the binomial (ErdÅ‘sRÃ©nyi) graph. 
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439 The graph is composed of two partitions. Set A has nodes 0 to 
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440 (n  1) and set B has nodes n to (n + m  1). 
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441 
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442 Parameters 
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443  
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444 n : int 
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445 The number of nodes in the first bipartite set. 
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446 m : int 
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447 The number of nodes in the second bipartite set. 
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448 p : float 
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449 Probability for edge creation. 
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450 seed : integer, random_state, or None (default) 
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451 Indicator of random number generation state. 
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452 See :ref:`Randomness<randomness>`. 
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453 directed : bool, optional (default=False) 
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454 If True return a directed graph 
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455 
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456 Notes 
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457  
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458 The bipartite random graph algorithm chooses each of the n*m (undirected) 
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459 or 2*nm (directed) possible edges with probability p. 
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460 
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461 This algorithm is $O(n+m)$ where $m$ is the expected number of edges. 
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462 
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463 The nodes are assigned the attribute 'bipartite' with the value 0 or 1 
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464 to indicate which bipartite set the node belongs to. 
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465 
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466 This function is not imported in the main namespace. 
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467 To use it use nx.bipartite.random_graph 
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468 
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469 See Also 
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470  
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471 gnp_random_graph, configuration_model 
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472 
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473 References 
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474  
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475 .. [1] Vladimir Batagelj and Ulrik Brandes, 
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476 "Efficient generation of large random networks", 
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477 Phys. Rev. E, 71, 036113, 2005. 
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478 """ 
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479 G = nx.Graph() 
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480 G = _add_nodes_with_bipartite_label(G, n, m) 
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481 if directed: 
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482 G = nx.DiGraph(G) 
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483 G.name = f"fast_gnp_random_graph({n},{m},{p})" 
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484 
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485 if p <= 0: 
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486 return G 
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487 if p >= 1: 
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488 return nx.complete_bipartite_graph(n, m) 
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489 
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490 lp = math.log(1.0  p) 
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491 
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492 v = 0 
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493 w = 1 
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494 while v < n: 
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495 lr = math.log(1.0  seed.random()) 
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496 w = w + 1 + int(lr / lp) 
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497 while w >= m and v < n: 
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498 w = w  m 
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499 v = v + 1 
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500 if v < n: 
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501 G.add_edge(v, n + w) 
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502 
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503 if directed: 
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504 # use the same algorithm to 
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505 # add edges from the "m" to "n" set 
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506 v = 0 
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507 w = 1 
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508 while v < n: 
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509 lr = math.log(1.0  seed.random()) 
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510 w = w + 1 + int(lr / lp) 
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511 while w >= m and v < n: 
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512 w = w  m 
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513 v = v + 1 
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514 if v < n: 
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515 G.add_edge(n + w, v) 
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516 
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517 return G 
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518 
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519 
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520 @py_random_state(3) 
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521 def gnmk_random_graph(n, m, k, seed=None, directed=False): 
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522 """Returns a random bipartite graph G_{n,m,k}. 
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523 
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524 Produces a bipartite graph chosen randomly out of the set of all graphs 
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525 with n top nodes, m bottom nodes, and k edges. 
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526 The graph is composed of two sets of nodes. 
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527 Set A has nodes 0 to (n  1) and set B has nodes n to (n + m  1). 
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528 
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529 Parameters 
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530  
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531 n : int 
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532 The number of nodes in the first bipartite set. 
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533 m : int 
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534 The number of nodes in the second bipartite set. 
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535 k : int 
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536 The number of edges 
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537 seed : integer, random_state, or None (default) 
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538 Indicator of random number generation state. 
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539 See :ref:`Randomness<randomness>`. 
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540 directed : bool, optional (default=False) 
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541 If True return a directed graph 
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542 
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543 Examples 
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544  
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545 from nx.algorithms import bipartite 
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546 G = bipartite.gnmk_random_graph(10,20,50) 
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547 
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548 See Also 
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549  
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550 gnm_random_graph 
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551 
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552 Notes 
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553  
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554 If k > m * n then a complete bipartite graph is returned. 
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555 
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556 This graph is a bipartite version of the `G_{nm}` random graph model. 
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557 
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558 The nodes are assigned the attribute 'bipartite' with the value 0 or 1 
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559 to indicate which bipartite set the node belongs to. 
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560 
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561 This function is not imported in the main namespace. 
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562 To use it use nx.bipartite.gnmk_random_graph 
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563 """ 
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564 G = nx.Graph() 
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565 G = _add_nodes_with_bipartite_label(G, n, m) 
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566 if directed: 
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567 G = nx.DiGraph(G) 
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568 G.name = f"bipartite_gnm_random_graph({n},{m},{k})" 
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569 if n == 1 or m == 1: 
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570 return G 
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571 max_edges = n * m # max_edges for bipartite networks 
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572 if k >= max_edges: # Maybe we should raise an exception here 
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573 return nx.complete_bipartite_graph(n, m, create_using=G) 
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574 
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575 top = [n for n, d in G.nodes(data=True) if d["bipartite"] == 0] 
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576 bottom = list(set(G)  set(top)) 
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577 edge_count = 0 
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578 while edge_count < k: 
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579 # generate random edge,u,v 
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580 u = seed.choice(top) 
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581 v = seed.choice(bottom) 
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582 if v in G[u]: 
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583 continue 
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584 else: 
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585 G.add_edge(u, v) 
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586 edge_count += 1 
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587 return G 
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588 
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589 
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590 def _add_nodes_with_bipartite_label(G, lena, lenb): 
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591 G.add_nodes_from(range(0, lena + lenb)) 
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592 b = dict(zip(range(0, lena), [0] * lena)) 
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593 b.update(dict(zip(range(lena, lena + lenb), [1] * lenb))) 
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset

594 nx.set_node_attributes(G, b, "bipartite") 
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset

595 return G 