Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/generators/directed.py @ 0:4f3585e2f14b draft default tip
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author | shellac |
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date | Mon, 22 Mar 2021 18:12:50 +0000 |
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1 """ |
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2 Generators for some directed graphs, including growing network (GN) graphs and |
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3 scale-free graphs. |
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4 |
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5 """ |
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6 |
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7 from collections import Counter |
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8 |
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9 import networkx as nx |
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10 from networkx.generators.classic import empty_graph |
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11 from networkx.utils import discrete_sequence |
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12 from networkx.utils import weighted_choice |
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13 from networkx.utils import py_random_state |
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14 |
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15 __all__ = [ |
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16 "gn_graph", |
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17 "gnc_graph", |
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18 "gnr_graph", |
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19 "random_k_out_graph", |
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20 "scale_free_graph", |
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21 ] |
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22 |
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23 |
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24 @py_random_state(3) |
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25 def gn_graph(n, kernel=None, create_using=None, seed=None): |
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26 """Returns the growing network (GN) digraph with `n` nodes. |
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27 |
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28 The GN graph is built by adding nodes one at a time with a link to one |
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29 previously added node. The target node for the link is chosen with |
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30 probability based on degree. The default attachment kernel is a linear |
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31 function of the degree of a node. |
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32 |
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33 The graph is always a (directed) tree. |
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34 |
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35 Parameters |
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36 ---------- |
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37 n : int |
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38 The number of nodes for the generated graph. |
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39 kernel : function |
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40 The attachment kernel. |
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41 create_using : NetworkX graph constructor, optional (default DiGraph) |
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42 Graph type to create. If graph instance, then cleared before populated. |
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43 seed : integer, random_state, or None (default) |
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44 Indicator of random number generation state. |
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45 See :ref:`Randomness<randomness>`. |
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46 |
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47 Examples |
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48 -------- |
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49 To create the undirected GN graph, use the :meth:`~DiGraph.to_directed` |
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50 method:: |
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51 |
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52 >>> D = nx.gn_graph(10) # the GN graph |
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53 >>> G = D.to_undirected() # the undirected version |
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54 |
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55 To specify an attachment kernel, use the `kernel` keyword argument:: |
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56 |
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57 >>> D = nx.gn_graph(10, kernel=lambda x: x ** 1.5) # A_k = k^1.5 |
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58 |
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59 References |
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60 ---------- |
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61 .. [1] P. L. Krapivsky and S. Redner, |
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62 Organization of Growing Random Networks, |
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63 Phys. Rev. E, 63, 066123, 2001. |
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64 """ |
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65 G = empty_graph(1, create_using, default=nx.DiGraph) |
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66 if not G.is_directed(): |
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67 raise nx.NetworkXError("create_using must indicate a Directed Graph") |
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68 |
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69 if kernel is None: |
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70 |
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71 def kernel(x): |
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72 return x |
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73 |
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74 if n == 1: |
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75 return G |
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76 |
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77 G.add_edge(1, 0) # get started |
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78 ds = [1, 1] # degree sequence |
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79 |
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80 for source in range(2, n): |
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81 # compute distribution from kernel and degree |
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82 dist = [kernel(d) for d in ds] |
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83 # choose target from discrete distribution |
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84 target = discrete_sequence(1, distribution=dist, seed=seed)[0] |
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85 G.add_edge(source, target) |
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86 ds.append(1) # the source has only one link (degree one) |
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87 ds[target] += 1 # add one to the target link degree |
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88 return G |
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89 |
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90 |
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91 @py_random_state(3) |
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92 def gnr_graph(n, p, create_using=None, seed=None): |
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93 """Returns the growing network with redirection (GNR) digraph with `n` |
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94 nodes and redirection probability `p`. |
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95 |
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96 The GNR graph is built by adding nodes one at a time with a link to one |
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97 previously added node. The previous target node is chosen uniformly at |
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98 random. With probabiliy `p` the link is instead "redirected" to the |
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99 successor node of the target. |
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100 |
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101 The graph is always a (directed) tree. |
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102 |
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103 Parameters |
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104 ---------- |
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105 n : int |
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106 The number of nodes for the generated graph. |
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107 p : float |
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108 The redirection probability. |
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109 create_using : NetworkX graph constructor, optional (default DiGraph) |
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110 Graph type to create. If graph instance, then cleared before populated. |
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111 seed : integer, random_state, or None (default) |
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112 Indicator of random number generation state. |
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113 See :ref:`Randomness<randomness>`. |
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114 |
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115 Examples |
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116 -------- |
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117 To create the undirected GNR graph, use the :meth:`~DiGraph.to_directed` |
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118 method:: |
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119 |
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120 >>> D = nx.gnr_graph(10, 0.5) # the GNR graph |
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121 >>> G = D.to_undirected() # the undirected version |
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122 |
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123 References |
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124 ---------- |
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125 .. [1] P. L. Krapivsky and S. Redner, |
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126 Organization of Growing Random Networks, |
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127 Phys. Rev. E, 63, 066123, 2001. |
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128 """ |
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129 G = empty_graph(1, create_using, default=nx.DiGraph) |
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130 if not G.is_directed(): |
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131 raise nx.NetworkXError("create_using must indicate a Directed Graph") |
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132 |
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133 if n == 1: |
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134 return G |
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135 |
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136 for source in range(1, n): |
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137 target = seed.randrange(0, source) |
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138 if seed.random() < p and target != 0: |
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139 target = next(G.successors(target)) |
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140 G.add_edge(source, target) |
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141 return G |
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142 |
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143 |
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144 @py_random_state(2) |
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145 def gnc_graph(n, create_using=None, seed=None): |
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146 """Returns the growing network with copying (GNC) digraph with `n` nodes. |
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147 |
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148 The GNC graph is built by adding nodes one at a time with a link to one |
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149 previously added node (chosen uniformly at random) and to all of that |
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150 node's successors. |
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151 |
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152 Parameters |
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153 ---------- |
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154 n : int |
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155 The number of nodes for the generated graph. |
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156 create_using : NetworkX graph constructor, optional (default DiGraph) |
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157 Graph type to create. If graph instance, then cleared before populated. |
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158 seed : integer, random_state, or None (default) |
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159 Indicator of random number generation state. |
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160 See :ref:`Randomness<randomness>`. |
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161 |
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162 References |
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163 ---------- |
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164 .. [1] P. L. Krapivsky and S. Redner, |
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165 Network Growth by Copying, |
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166 Phys. Rev. E, 71, 036118, 2005k.}, |
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167 """ |
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168 G = empty_graph(1, create_using, default=nx.DiGraph) |
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169 if not G.is_directed(): |
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170 raise nx.NetworkXError("create_using must indicate a Directed Graph") |
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171 |
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172 if n == 1: |
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173 return G |
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174 |
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175 for source in range(1, n): |
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176 target = seed.randrange(0, source) |
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177 for succ in G.successors(target): |
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178 G.add_edge(source, succ) |
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179 G.add_edge(source, target) |
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180 return G |
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181 |
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182 |
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183 @py_random_state(7) |
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184 def scale_free_graph( |
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185 n, |
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186 alpha=0.41, |
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187 beta=0.54, |
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188 gamma=0.05, |
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189 delta_in=0.2, |
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190 delta_out=0, |
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191 create_using=None, |
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192 seed=None, |
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193 ): |
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194 """Returns a scale-free directed graph. |
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195 |
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196 Parameters |
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197 ---------- |
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198 n : integer |
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199 Number of nodes in graph |
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200 alpha : float |
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201 Probability for adding a new node connected to an existing node |
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202 chosen randomly according to the in-degree distribution. |
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203 beta : float |
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204 Probability for adding an edge between two existing nodes. |
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205 One existing node is chosen randomly according the in-degree |
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206 distribution and the other chosen randomly according to the out-degree |
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207 distribution. |
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208 gamma : float |
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209 Probability for adding a new node connected to an existing node |
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210 chosen randomly according to the out-degree distribution. |
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211 delta_in : float |
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212 Bias for choosing nodes from in-degree distribution. |
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213 delta_out : float |
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214 Bias for choosing nodes from out-degree distribution. |
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215 create_using : NetworkX graph constructor, optional |
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216 The default is a MultiDiGraph 3-cycle. |
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217 If a graph instance, use it without clearing first. |
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218 If a graph constructor, call it to construct an empty graph. |
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219 seed : integer, random_state, or None (default) |
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220 Indicator of random number generation state. |
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221 See :ref:`Randomness<randomness>`. |
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222 |
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223 Examples |
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224 -------- |
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225 Create a scale-free graph on one hundred nodes:: |
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226 |
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227 >>> G = nx.scale_free_graph(100) |
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228 |
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229 Notes |
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230 ----- |
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231 The sum of `alpha`, `beta`, and `gamma` must be 1. |
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232 |
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233 References |
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234 ---------- |
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235 .. [1] B. Bollobás, C. Borgs, J. Chayes, and O. Riordan, |
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236 Directed scale-free graphs, |
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237 Proceedings of the fourteenth annual ACM-SIAM Symposium on |
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238 Discrete Algorithms, 132--139, 2003. |
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239 """ |
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240 |
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241 def _choose_node(G, distribution, delta, psum): |
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242 cumsum = 0.0 |
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243 # normalization |
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244 r = seed.random() |
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245 for n, d in distribution: |
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246 cumsum += (d + delta) / psum |
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247 if r < cumsum: |
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248 break |
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249 return n |
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250 |
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251 if create_using is None or not hasattr(create_using, "_adj"): |
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252 # start with 3-cycle |
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253 G = nx.empty_graph(3, create_using, default=nx.MultiDiGraph) |
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254 G.add_edges_from([(0, 1), (1, 2), (2, 0)]) |
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255 else: |
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256 G = create_using |
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257 if not (G.is_directed() and G.is_multigraph()): |
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258 raise nx.NetworkXError("MultiDiGraph required in create_using") |
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259 |
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260 if alpha <= 0: |
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261 raise ValueError("alpha must be > 0.") |
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262 if beta <= 0: |
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263 raise ValueError("beta must be > 0.") |
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264 if gamma <= 0: |
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265 raise ValueError("gamma must be > 0.") |
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266 |
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267 if abs(alpha + beta + gamma - 1.0) >= 1e-9: |
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268 raise ValueError("alpha+beta+gamma must equal 1.") |
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269 |
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270 number_of_edges = G.number_of_edges() |
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271 while len(G) < n: |
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272 psum_in = number_of_edges + delta_in * len(G) |
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273 psum_out = number_of_edges + delta_out * len(G) |
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274 r = seed.random() |
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275 # random choice in alpha,beta,gamma ranges |
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276 if r < alpha: |
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277 # alpha |
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278 # add new node v |
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279 v = len(G) |
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280 # choose w according to in-degree and delta_in |
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281 w = _choose_node(G, G.in_degree(), delta_in, psum_in) |
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282 elif r < alpha + beta: |
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283 # beta |
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284 # choose v according to out-degree and delta_out |
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285 v = _choose_node(G, G.out_degree(), delta_out, psum_out) |
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286 # choose w according to in-degree and delta_in |
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287 w = _choose_node(G, G.in_degree(), delta_in, psum_in) |
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288 else: |
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289 # gamma |
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290 # choose v according to out-degree and delta_out |
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291 v = _choose_node(G, G.out_degree(), delta_out, psum_out) |
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292 # add new node w |
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293 w = len(G) |
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294 G.add_edge(v, w) |
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295 number_of_edges += 1 |
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296 return G |
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297 |
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298 |
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299 @py_random_state(4) |
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300 def random_uniform_k_out_graph(n, k, self_loops=True, with_replacement=True, seed=None): |
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301 """Returns a random `k`-out graph with uniform attachment. |
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302 |
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303 A random `k`-out graph with uniform attachment is a multidigraph |
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304 generated by the following algorithm. For each node *u*, choose |
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305 `k` nodes *v* uniformly at random (with replacement). Add a |
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306 directed edge joining *u* to *v*. |
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307 |
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308 Parameters |
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309 ---------- |
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310 n : int |
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311 The number of nodes in the returned graph. |
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312 |
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313 k : int |
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314 The out-degree of each node in the returned graph. |
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315 |
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316 self_loops : bool |
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317 If True, self-loops are allowed when generating the graph. |
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318 |
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319 with_replacement : bool |
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320 If True, neighbors are chosen with replacement and the |
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321 returned graph will be a directed multigraph. Otherwise, |
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322 neighbors are chosen without replacement and the returned graph |
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323 will be a directed graph. |
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324 |
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325 seed : integer, random_state, or None (default) |
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326 Indicator of random number generation state. |
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327 See :ref:`Randomness<randomness>`. |
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328 |
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329 Returns |
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330 ------- |
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331 NetworkX graph |
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332 A `k`-out-regular directed graph generated according to the |
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333 above algorithm. It will be a multigraph if and only if |
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334 `with_replacement` is True. |
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335 |
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336 Raises |
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337 ------ |
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338 ValueError |
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339 If `with_replacement` is False and `k` is greater than |
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340 `n`. |
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341 |
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342 See also |
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343 -------- |
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344 random_k_out_graph |
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345 |
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346 Notes |
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347 ----- |
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348 The return digraph or multidigraph may not be strongly connected, or |
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349 even weakly connected. |
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350 |
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351 If `with_replacement` is True, this function is similar to |
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352 :func:`random_k_out_graph`, if that function had parameter `alpha` |
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353 set to positive infinity. |
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354 |
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355 """ |
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356 if with_replacement: |
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357 create_using = nx.MultiDiGraph() |
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358 |
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359 def sample(v, nodes): |
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360 if not self_loops: |
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361 nodes = nodes - {v} |
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362 return (seed.choice(list(nodes)) for i in range(k)) |
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363 |
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364 else: |
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365 create_using = nx.DiGraph() |
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366 |
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367 def sample(v, nodes): |
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368 if not self_loops: |
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369 nodes = nodes - {v} |
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370 return seed.sample(nodes, k) |
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371 |
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372 G = nx.empty_graph(n, create_using) |
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373 nodes = set(G) |
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374 for u in G: |
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375 G.add_edges_from((u, v) for v in sample(u, nodes)) |
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376 return G |
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377 |
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378 |
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379 @py_random_state(4) |
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380 def random_k_out_graph(n, k, alpha, self_loops=True, seed=None): |
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381 """Returns a random `k`-out graph with preferential attachment. |
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382 |
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383 A random `k`-out graph with preferential attachment is a |
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384 multidigraph generated by the following algorithm. |
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385 |
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386 1. Begin with an empty digraph, and initially set each node to have |
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387 weight `alpha`. |
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388 2. Choose a node `u` with out-degree less than `k` uniformly at |
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389 random. |
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390 3. Choose a node `v` from with probability proportional to its |
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391 weight. |
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392 4. Add a directed edge from `u` to `v`, and increase the weight |
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393 of `v` by one. |
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394 5. If each node has out-degree `k`, halt, otherwise repeat from |
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395 step 2. |
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396 |
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397 For more information on this model of random graph, see [1]. |
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398 |
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399 Parameters |
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400 ---------- |
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401 n : int |
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402 The number of nodes in the returned graph. |
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403 |
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404 k : int |
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405 The out-degree of each node in the returned graph. |
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406 |
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407 alpha : float |
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408 A positive :class:`float` representing the initial weight of |
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409 each vertex. A higher number means that in step 3 above, nodes |
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410 will be chosen more like a true uniformly random sample, and a |
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411 lower number means that nodes are more likely to be chosen as |
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412 their in-degree increases. If this parameter is not positive, a |
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413 :exc:`ValueError` is raised. |
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414 |
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415 self_loops : bool |
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416 If True, self-loops are allowed when generating the graph. |
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417 |
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418 seed : integer, random_state, or None (default) |
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419 Indicator of random number generation state. |
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420 See :ref:`Randomness<randomness>`. |
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421 |
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422 Returns |
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423 ------- |
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424 :class:`~networkx.classes.MultiDiGraph` |
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425 A `k`-out-regular multidigraph generated according to the above |
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426 algorithm. |
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427 |
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428 Raises |
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429 ------ |
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430 ValueError |
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431 If `alpha` is not positive. |
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432 |
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433 Notes |
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434 ----- |
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435 The returned multidigraph may not be strongly connected, or even |
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436 weakly connected. |
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437 |
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438 References |
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439 ---------- |
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440 [1]: Peterson, Nicholas R., and Boris Pittel. |
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441 "Distance between two random `k`-out digraphs, with and without |
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442 preferential attachment." |
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443 arXiv preprint arXiv:1311.5961 (2013). |
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444 <https://arxiv.org/abs/1311.5961> |
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445 |
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446 """ |
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447 if alpha < 0: |
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448 raise ValueError("alpha must be positive") |
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449 G = nx.empty_graph(n, create_using=nx.MultiDiGraph) |
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450 weights = Counter({v: alpha for v in G}) |
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451 for i in range(k * n): |
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452 u = seed.choice([v for v, d in G.out_degree() if d < k]) |
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453 # If self-loops are not allowed, make the source node `u` have |
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454 # weight zero. |
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455 if not self_loops: |
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456 adjustment = Counter({u: weights[u]}) |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
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457 else: |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
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458 adjustment = Counter() |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
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459 v = weighted_choice(weights - adjustment, seed=seed) |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
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460 G.add_edge(u, v) |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
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461 weights[v] += 1 |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
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462 return G |