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annotate planemo/lib/python3.7/site-packages/networkx/generators/duplication.py @ 1:56ad4e20f292 draft

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"planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
author guerler
date Fri, 31 Jul 2020 00:32:28 -0400
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1 # duplication.py - functions for generating graphs by duplicating nodes
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2 #
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3 # Copyright 2016-2019 NetworkX developers.
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4 # Copyright (C) 2004-2019 by
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5 # Aric Hagberg <hagberg@lanl.gov>
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6 # Dan Schult <dschult@colgate.edu>
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7 # Pieter Swart <swart@lanl.gov>
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8 #
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9 # This file is part of NetworkX.
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10 #
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11 # NetworkX is distributed under a BSD license; see LICENSE.txt for more
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12 # information.
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13 """Functions for generating graphs based on the "duplication" method.
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14
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15 These graph generators start with a small initial graph then duplicate
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16 nodes and (partially) duplicate their edges. These functions are
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17 generally inspired by biological networks.
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18
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19 """
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20 import networkx as nx
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21 from networkx.utils import py_random_state
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22 from networkx.exception import NetworkXError
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23
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24 __all__ = ['partial_duplication_graph', 'duplication_divergence_graph']
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25
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26
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27 @py_random_state(4)
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28 def partial_duplication_graph(N, n, p, q, seed=None):
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29 """Returns a random graph using the partial duplication model.
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30
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31 Parameters
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32 ----------
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33 N : int
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34 The total number of nodes in the final graph.
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35
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36 n : int
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37 The number of nodes in the initial clique.
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38
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39 p : float
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40 The probability of joining each neighbor of a node to the
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41 duplicate node. Must be a number in the between zero and one,
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42 inclusive.
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43
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44 q : float
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45 The probability of joining the source node to the duplicate
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46 node. Must be a number in the between zero and one, inclusive.
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47
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48 seed : integer, random_state, or None (default)
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49 Indicator of random number generation state.
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50 See :ref:`Randomness<randomness>`.
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51
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52 Notes
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53 -----
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54 A graph of nodes is grown by creating a fully connected graph
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55 of size `n`. The following procedure is then repeated until
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56 a total of `N` nodes have been reached.
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57
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58 1. A random node, *u*, is picked and a new node, *v*, is created.
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59 2. For each neighbor of *u* an edge from the neighbor to *v* is created
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60 with probability `p`.
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61 3. An edge from *u* to *v* is created with probability `q`.
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62
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63 This algorithm appears in [1].
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64
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65 This implementation allows the possibility of generating
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66 disconnected graphs.
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67
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68 References
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69 ----------
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70 .. [1] Knudsen Michael, and Carsten Wiuf. "A Markov chain approach to
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71 randomly grown graphs." Journal of Applied Mathematics 2008.
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72 <https://doi.org/10.1155/2008/190836>
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73
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74 """
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75 if p < 0 or p > 1 or q < 0 or q > 1:
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76 msg = "partial duplication graph must have 0 <= p, q <= 1."
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77 raise NetworkXError(msg)
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78 if n > N:
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79 raise NetworkXError("partial duplication graph must have n <= N.")
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80
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81 G = nx.complete_graph(n)
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82 for new_node in range(n, N):
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83 # Pick a random vertex, u, already in the graph.
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84 src_node = seed.randint(0, new_node - 1)
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85
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86 # Add a new vertex, v, to the graph.
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87 G.add_node(new_node)
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88
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89 # For each neighbor of u...
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90 for neighbor_node in list(nx.all_neighbors(G, src_node)):
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91 # Add the neighbor to v with probability p.
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92 if seed.random() < p:
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93 G.add_edge(new_node, neighbor_node)
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94
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95 # Join v and u with probability q.
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96 if seed.random() < q:
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97 G.add_edge(new_node, src_node)
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98 return G
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99
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100
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101 @py_random_state(2)
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102 def duplication_divergence_graph(n, p, seed=None):
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103 """Returns an undirected graph using the duplication-divergence model.
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104
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105 A graph of `n` nodes is created by duplicating the initial nodes
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106 and retaining edges incident to the original nodes with a retention
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107 probability `p`.
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108
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109 Parameters
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110 ----------
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111 n : int
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112 The desired number of nodes in the graph.
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113 p : float
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114 The probability for retaining the edge of the replicated node.
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115 seed : integer, random_state, or None (default)
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116 Indicator of random number generation state.
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117 See :ref:`Randomness<randomness>`.
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118
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119 Returns
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120 -------
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121 G : Graph
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122
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123 Raises
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124 ------
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125 NetworkXError
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126 If `p` is not a valid probability.
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127 If `n` is less than 2.
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128
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129 Notes
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130 -----
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131 This algorithm appears in [1].
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132
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133 This implementation disallows the possibility of generating
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134 disconnected graphs.
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135
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136 References
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137 ----------
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138 .. [1] I. Ispolatov, P. L. Krapivsky, A. Yuryev,
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139 "Duplication-divergence model of protein interaction network",
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140 Phys. Rev. E, 71, 061911, 2005.
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141
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142 """
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143 if p > 1 or p < 0:
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144 msg = "NetworkXError p={0} is not in [0,1].".format(p)
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145 raise nx.NetworkXError(msg)
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146 if n < 2:
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147 msg = 'n must be greater than or equal to 2'
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148 raise nx.NetworkXError(msg)
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149
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150 G = nx.Graph()
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151
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152 # Initialize the graph with two connected nodes.
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153 G.add_edge(0, 1)
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154 i = 2
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155 while i < n:
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156 # Choose a random node from current graph to duplicate.
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157 random_node = seed.choice(list(G))
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158 # Make the replica.
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159 G.add_node(i)
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160 # flag indicates whether at least one edge is connected on the replica.
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161 flag = False
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162 for nbr in G.neighbors(random_node):
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163 if seed.random() < p:
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164 # Link retention step.
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165 G.add_edge(i, nbr)
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166 flag = True
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167 if not flag:
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168 # Delete replica if no edges retained.
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169 G.remove_node(i)
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170 else:
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171 # Successful duplication.
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172 i += 1
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173 return G