Mercurial > repos > guerler > springsuite

annotate planemo/lib/python3.7/site-packages/networkx/generators/small.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
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1 # -*- coding: utf-8 -*-
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2 """
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3 Various small and named graphs, together with some compact generators.
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4
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5 """
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6 __author__ = """Aric Hagberg (hagberg@lanl.gov)\nPieter Swart (swart@lanl.gov)"""
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7 # Copyright (C) 2004-2019 by
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8 # Aric Hagberg <hagberg@lanl.gov>
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9 # Dan Schult <dschult@colgate.edu>
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10 # Pieter Swart <swart@lanl.gov>
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11 # All rights reserved.
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12 # BSD license.
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13
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14 __all__ = ['make_small_graph',
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15 'LCF_graph',
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16 'bull_graph',
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17 'chvatal_graph',
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18 'cubical_graph',
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19 'desargues_graph',
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20 'diamond_graph',
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21 'dodecahedral_graph',
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22 'frucht_graph',
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23 'heawood_graph',
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24 'hoffman_singleton_graph',
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25 'house_graph',
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26 'house_x_graph',
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27 'icosahedral_graph',
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28 'krackhardt_kite_graph',
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29 'moebius_kantor_graph',
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30 'octahedral_graph',
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31 'pappus_graph',
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32 'petersen_graph',
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33 'sedgewick_maze_graph',
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34 'tetrahedral_graph',
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35 'truncated_cube_graph',
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36 'truncated_tetrahedron_graph',
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37 'tutte_graph']
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38
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39 import networkx as nx
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40 from networkx.generators.classic import empty_graph, cycle_graph, path_graph, complete_graph
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41 from networkx.exception import NetworkXError
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42
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43 #------------------------------------------------------------------------------
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44 # Tools for creating small graphs
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45 #------------------------------------------------------------------------------
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46
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47
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48 def make_small_undirected_graph(graph_description, create_using=None):
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49 """
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50 Return a small undirected graph described by graph_description.
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51
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52 See make_small_graph.
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53 """
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54 G = empty_graph(0, create_using)
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55 if G.is_directed():
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56 raise NetworkXError("Directed Graph not supported")
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57 return make_small_graph(graph_description, G)
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58
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59
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60 def make_small_graph(graph_description, create_using=None):
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61 """
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62 Return the small graph described by graph_description.
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63
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64 graph_description is a list of the form [ltype,name,n,xlist]
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65
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66 Here ltype is one of "adjacencylist" or "edgelist",
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67 name is the name of the graph and n the number of nodes.
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68 This constructs a graph of n nodes with integer labels 0,..,n-1.
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69
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70 If ltype="adjacencylist" then xlist is an adjacency list
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71 with exactly n entries, in with the j'th entry (which can be empty)
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72 specifies the nodes connected to vertex j.
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73 e.g. the "square" graph C_4 can be obtained by
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74
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75 >>> G=nx.make_small_graph(["adjacencylist","C_4",4,[[2,4],[1,3],[2,4],[1,3]]])
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76
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77 or, since we do not need to add edges twice,
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78
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79 >>> G=nx.make_small_graph(["adjacencylist","C_4",4,[[2,4],[3],[4],[]]])
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80
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81 If ltype="edgelist" then xlist is an edge list
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82 written as [[v1,w2],[v2,w2],...,[vk,wk]],
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83 where vj and wj integers in the range 1,..,n
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84 e.g. the "square" graph C_4 can be obtained by
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85
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86 >>> G=nx.make_small_graph(["edgelist","C_4",4,[[1,2],[3,4],[2,3],[4,1]]])
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87
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88 Use the create_using argument to choose the graph class/type.
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89 """
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90 ltype = graph_description[0]
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91 name = graph_description[1]
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92 n = graph_description[2]
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93
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94 G = empty_graph(n, create_using)
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95 nodes = G.nodes()
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96
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97 if ltype == "adjacencylist":
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98 adjlist = graph_description[3]
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99 if len(adjlist) != n:
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100 raise NetworkXError("invalid graph_description")
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101 G.add_edges_from([(u - 1, v) for v in nodes for u in adjlist[v]])
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102 elif ltype == "edgelist":
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103 edgelist = graph_description[3]
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104 for e in edgelist:
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105 v1 = e[0] - 1
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106 v2 = e[1] - 1
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107 if v1 < 0 or v1 > n - 1 or v2 < 0 or v2 > n - 1:
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108 raise NetworkXError("invalid graph_description")
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109 else:
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110 G.add_edge(v1, v2)
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111 G.name = name
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112 return G
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113
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114
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115 def LCF_graph(n, shift_list, repeats, create_using=None):
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116 """
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117 Return the cubic graph specified in LCF notation.
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118
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119 LCF notation (LCF=Lederberg-Coxeter-Fruchte) is a compressed
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120 notation used in the generation of various cubic Hamiltonian
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121 graphs of high symmetry. See, for example, dodecahedral_graph,
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122 desargues_graph, heawood_graph and pappus_graph below.
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123
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124 n (number of nodes)
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125 The starting graph is the n-cycle with nodes 0,...,n-1.
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126 (The null graph is returned if n < 0.)
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127
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128 shift_list = [s1,s2,..,sk], a list of integer shifts mod n,
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129
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130 repeats
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131 integer specifying the number of times that shifts in shift_list
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132 are successively applied to each v_current in the n-cycle
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133 to generate an edge between v_current and v_current+shift mod n.
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134
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135 For v1 cycling through the n-cycle a total of k*repeats
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136 with shift cycling through shiftlist repeats times connect
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137 v1 with v1+shift mod n
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138
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139 The utility graph $K_{3,3}$
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140
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141 >>> G = nx.LCF_graph(6, [3, -3], 3)
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142
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143 The Heawood graph
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144
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145 >>> G = nx.LCF_graph(14, [5, -5], 7)
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146
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147 See http://mathworld.wolfram.com/LCFNotation.html for a description
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148 and references.
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149
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150 """
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151 if n <= 0:
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152 return empty_graph(0, create_using)
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153
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154 # start with the n-cycle
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155 G = cycle_graph(n, create_using)
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156 if G.is_directed():
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157 raise NetworkXError("Directed Graph not supported")
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158 G.name = "LCF_graph"
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159 nodes = sorted(list(G))
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160
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161 n_extra_edges = repeats * len(shift_list)
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162 # edges are added n_extra_edges times
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163 # (not all of these need be new)
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164 if n_extra_edges < 1:
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165 return G
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166
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167 for i in range(n_extra_edges):
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168 shift = shift_list[i % len(shift_list)] # cycle through shift_list
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169 v1 = nodes[i % n] # cycle repeatedly through nodes
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170 v2 = nodes[(i + shift) % n]
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171 G.add_edge(v1, v2)
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172 return G
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173
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174
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175 #-------------------------------------------------------------------------------
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176 # Various small and named graphs
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177 #-------------------------------------------------------------------------------
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178
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179 def bull_graph(create_using=None):
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180 """Returns the Bull graph. """
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181 description = [
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182 "adjacencylist",
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183 "Bull Graph",
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184 5,
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185 [[2, 3], [1, 3, 4], [1, 2, 5], [2], [3]]
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186 ]
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187 G = make_small_undirected_graph(description, create_using)
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188 return G
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189
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190
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191 def chvatal_graph(create_using=None):
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192 """Returns the Chvátal graph."""
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193 description = [
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194 "adjacencylist",
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195 "Chvatal Graph",
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196 12,
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197 [[2, 5, 7, 10], [3, 6, 8], [4, 7, 9], [5, 8, 10],
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198 [6, 9], [11, 12], [11, 12], [9, 12],
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199 [11], [11, 12], [], []]
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200 ]
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201 G = make_small_undirected_graph(description, create_using)
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202 return G
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203
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204
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205 def cubical_graph(create_using=None):
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206 """Returns the 3-regular Platonic Cubical graph."""
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207 description = [
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208 "adjacencylist",
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209 "Platonic Cubical Graph",
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210 8,
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211 [[2, 4, 5], [1, 3, 8], [2, 4, 7], [1, 3, 6],
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212 [1, 6, 8], [4, 5, 7], [3, 6, 8], [2, 5, 7]]
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213 ]
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214 G = make_small_undirected_graph(description, create_using)
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215 return G
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216
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217
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218 def desargues_graph(create_using=None):
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219 """ Return the Desargues graph."""
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220 G = LCF_graph(20, [5, -5, 9, -9], 5, create_using)
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221 G.name = "Desargues Graph"
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222 return G
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223
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224
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225 def diamond_graph(create_using=None):
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226 """Returns the Diamond graph. """
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227 description = [
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228 "adjacencylist",
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229 "Diamond Graph",
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230 4,
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231 [[2, 3], [1, 3, 4], [1, 2, 4], [2, 3]]
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232 ]
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233 G = make_small_undirected_graph(description, create_using)
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234 return G
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235
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236
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237 def dodecahedral_graph(create_using=None):
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238 """ Return the Platonic Dodecahedral graph. """
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239 G = LCF_graph(20, [10, 7, 4, -4, -7, 10, -4, 7, -7, 4], 2, create_using)
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240 G.name = "Dodecahedral Graph"
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241 return G
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242
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243
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244 def frucht_graph(create_using=None):
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245 """Returns the Frucht Graph.
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246
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247 The Frucht Graph is the smallest cubical graph whose
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248 automorphism group consists only of the identity element.
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249
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250 """
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251 G = cycle_graph(7, create_using)
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252 G.add_edges_from([[0, 7], [1, 7], [2, 8], [3, 9], [4, 9], [5, 10], [6, 10],
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253 [7, 11], [8, 11], [8, 9], [10, 11]])
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254
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255 G.name = "Frucht Graph"
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256 return G
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257
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258
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259 def heawood_graph(create_using=None):
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260 """ Return the Heawood graph, a (3,6) cage. """
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261 G = LCF_graph(14, [5, -5], 7, create_using)
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262 G.name = "Heawood Graph"
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263 return G
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264
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265
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266 def hoffman_singleton_graph():
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267 '''Return the Hoffman-Singleton Graph.'''
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268 G = nx.Graph()
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269 for i in range(5):
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270 for j in range(5):
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271 G.add_edge(('pentagon', i, j), ('pentagon', i, (j - 1) % 5))
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272 G.add_edge(('pentagon', i, j), ('pentagon', i, (j + 1) % 5))
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273 G.add_edge(('pentagram', i, j), ('pentagram', i, (j - 2) % 5))
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274 G.add_edge(('pentagram', i, j), ('pentagram', i, (j + 2) % 5))
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275 for k in range(5):
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276 G.add_edge(('pentagon', i, j),
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277 ('pentagram', k, (i * k + j) % 5))
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278 G = nx.convert_node_labels_to_integers(G)
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279 G.name = 'Hoffman-Singleton Graph'
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280 return G
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281
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282
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283 def house_graph(create_using=None):
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284 """Returns the House graph (square with triangle on top)."""
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285 description = [
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286 "adjacencylist",
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287 "House Graph",
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288 5,
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289 [[2, 3], [1, 4], [1, 4, 5], [2, 3, 5], [3, 4]]
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290 ]
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291 G = make_small_undirected_graph(description, create_using)
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292 return G
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293
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294
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295 def house_x_graph(create_using=None):
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296 """Returns the House graph with a cross inside the house square."""
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297 description = [
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298 "adjacencylist",
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299 "House-with-X-inside Graph",
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300 5,
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301 [[2, 3, 4], [1, 3, 4], [1, 2, 4, 5], [1, 2, 3, 5], [3, 4]]
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302 ]
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303 G = make_small_undirected_graph(description, create_using)
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304 return G
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305
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306
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307 def icosahedral_graph(create_using=None):
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308 """Returns the Platonic Icosahedral graph."""
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309 description = [
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310 "adjacencylist",
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311 "Platonic Icosahedral Graph",
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312 12,
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313 [[2, 6, 8, 9, 12], [3, 6, 7, 9], [4, 7, 9, 10], [5, 7, 10, 11],
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314 [6, 7, 11, 12], [7, 12], [], [9, 10, 11, 12],
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315 [10], [11], [12], []]
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316 ]
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317 G = make_small_undirected_graph(description, create_using)
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318 return G
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319
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320
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321 def krackhardt_kite_graph(create_using=None):
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322 """
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323 Return the Krackhardt Kite Social Network.
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324
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325 A 10 actor social network introduced by David Krackhardt
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326 to illustrate: degree, betweenness, centrality, closeness, etc.
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327 The traditional labeling is:
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328 Andre=1, Beverley=2, Carol=3, Diane=4,
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329 Ed=5, Fernando=6, Garth=7, Heather=8, Ike=9, Jane=10.
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330
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331 """
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332 description = [
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333 "adjacencylist",
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334 "Krackhardt Kite Social Network",
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335 10,
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336 [[2, 3, 4, 6], [1, 4, 5, 7], [1, 4, 6], [1, 2, 3, 5, 6, 7], [2, 4, 7],
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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337 [1, 3, 4, 7, 8], [2, 4, 5, 6, 8], [6, 7, 9], [8, 10], [9]]
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338 ]
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339 G = make_small_undirected_graph(description, create_using)
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340 return G
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341
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342
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343 def moebius_kantor_graph(create_using=None):
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344 """Returns the Moebius-Kantor graph."""
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345 G = LCF_graph(16, [5, -5], 8, create_using)
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346 G.name = "Moebius-Kantor Graph"
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347 return G
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348
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349
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350 def octahedral_graph(create_using=None):
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351 """Returns the Platonic Octahedral graph."""
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352 description = [
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353 "adjacencylist",
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354 "Platonic Octahedral Graph",
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355 6,
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356 [[2, 3, 4, 5], [3, 4, 6], [5, 6], [5, 6], [6], []]
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357 ]
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358 G = make_small_undirected_graph(description, create_using)
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359 return G
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360
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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361
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362 def pappus_graph():
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363 """ Return the Pappus graph."""
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364 G = LCF_graph(18, [5, 7, -7, 7, -7, -5], 3)
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365 G.name = "Pappus Graph"
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366 return G
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367
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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368
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369 def petersen_graph(create_using=None):
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370 """Returns the Petersen graph."""
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371 description = [
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372 "adjacencylist",
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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373 "Petersen Graph",
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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374 10,
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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375 [[2, 5, 6], [1, 3, 7], [2, 4, 8], [3, 5, 9], [4, 1, 10], [1, 8, 9], [2, 9, 10],
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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376 [3, 6, 10], [4, 6, 7], [5, 7, 8]]
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377 ]
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378 G = make_small_undirected_graph(description, create_using)
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379 return G
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380
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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381
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382 def sedgewick_maze_graph(create_using=None):
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383 """
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384 Return a small maze with a cycle.
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385
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386 This is the maze used in Sedgewick,3rd Edition, Part 5, Graph
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387 Algorithms, Chapter 18, e.g. Figure 18.2 and following.
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388 Nodes are numbered 0,..,7
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389 """
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390 G = empty_graph(0, create_using)
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391 G.add_nodes_from(range(8))
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392 G.add_edges_from([[0, 2], [0, 7], [0, 5]])
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393 G.add_edges_from([[1, 7], [2, 6]])
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394 G.add_edges_from([[3, 4], [3, 5]])
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395 G.add_edges_from([[4, 5], [4, 7], [4, 6]])
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396 G.name = "Sedgewick Maze"
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397 return G
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398
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399
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400 def tetrahedral_graph(create_using=None):
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401 """ Return the 3-regular Platonic Tetrahedral graph."""
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402 G = complete_graph(4, create_using)
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403 G.name = "Platonic Tetrahedral graph"
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404 return G
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405
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406
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407 def truncated_cube_graph(create_using=None):
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408 """Returns the skeleton of the truncated cube."""
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409 description = [
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410 "adjacencylist",
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411 "Truncated Cube Graph",
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412 24,
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413 [[2, 3, 5], [12, 15], [4, 5], [7, 9],
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414 [6], [17, 19], [8, 9], [11, 13],
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415 [10], [18, 21], [12, 13], [15],
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416 [14], [22, 23], [16], [20, 24],
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417 [18, 19], [21], [20], [24],
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418 [22], [23], [24], []]
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419 ]
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420 G = make_small_undirected_graph(description, create_using)
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421 return G
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422
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423
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424 def truncated_tetrahedron_graph(create_using=None):
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425 """Returns the skeleton of the truncated Platonic tetrahedron."""
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426 G = path_graph(12, create_using)
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427 # G.add_edges_from([(1,3),(1,10),(2,7),(4,12),(5,12),(6,8),(9,11)])
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428 G.add_edges_from([(0, 2), (0, 9), (1, 6), (3, 11), (4, 11), (5, 7), (8, 10)])
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429 G.name = "Truncated Tetrahedron Graph"
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430 return G
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431
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432
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433 def tutte_graph(create_using=None):
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434 """Returns the Tutte graph."""
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435 description = [
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436 "adjacencylist",
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437 "Tutte's Graph",
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438 46,
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439 [[2, 3, 4], [5, 27], [11, 12], [19, 20], [6, 34],
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440 [7, 30], [8, 28], [9, 15], [10, 39], [11, 38],
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441 [40], [13, 40], [14, 36], [15, 16], [35],
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442 [17, 23], [18, 45], [19, 44], [46], [21, 46],
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443 [22, 42], [23, 24], [41], [25, 28], [26, 33],
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444 [27, 32], [34], [29], [30, 33], [31],
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445 [32, 34], [33], [], [], [36, 39],
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446 [37], [38, 40], [39], [], [],
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447 [42, 45], [43], [44, 46], [45], [], []]
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448 ]
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449 G = make_small_undirected_graph(description, create_using)
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450 return G