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annotate planemo/lib/python3.7/site-packages/networkx/generators/classic.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 # Copyright (C) 2004-2019 by
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2 # Aric Hagberg <hagberg@lanl.gov>
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3 # Dan Schult <dschult@colgate.edu>
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4 # Pieter Swart <swart@lanl.gov>
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5 # All rights reserved.
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6 # BSD license.
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7 #
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8 # Authors: Aric Hagberg (hagberg@lanl.gov)
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9 # Pieter Swart (swart@lanl.gov)
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10 """Generators for some classic graphs.
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11
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12 The typical graph generator is called as follows:
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13
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14 >>> G = nx.complete_graph(100)
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15
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16 returning the complete graph on n nodes labeled 0, .., 99
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17 as a simple graph. Except for empty_graph, all the generators
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18 in this module return a Graph class (i.e. a simple, undirected graph).
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19
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20 """
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21
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22 import itertools
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23
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24 import networkx as nx
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25 from networkx.classes import Graph
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26 from networkx.exception import NetworkXError
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27 from networkx.utils import accumulate
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28 from networkx.utils import nodes_or_number
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29 from networkx.utils import pairwise
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30
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31 __all__ = ['balanced_tree',
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32 'barbell_graph',
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33 'binomial_tree',
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34 'complete_graph',
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35 'complete_multipartite_graph',
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36 'circular_ladder_graph',
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37 'circulant_graph',
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38 'cycle_graph',
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39 'dorogovtsev_goltsev_mendes_graph',
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40 'empty_graph',
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41 'full_rary_tree',
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42 'ladder_graph',
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43 'lollipop_graph',
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44 'null_graph',
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45 'path_graph',
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46 'star_graph',
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47 'trivial_graph',
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48 'turan_graph',
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49 'wheel_graph']
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50
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51
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52 # -------------------------------------------------------------------
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53 # Some Classic Graphs
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54 # -------------------------------------------------------------------
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55
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56 def _tree_edges(n, r):
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57 if n == 0:
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58 return
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59 # helper function for trees
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60 # yields edges in rooted tree at 0 with n nodes and branching ratio r
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61 nodes = iter(range(n))
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62 parents = [next(nodes)] # stack of max length r
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63 while parents:
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64 source = parents.pop(0)
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65 for i in range(r):
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66 try:
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67 target = next(nodes)
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68 parents.append(target)
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69 yield source, target
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70 except StopIteration:
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71 break
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72
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73
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74 def full_rary_tree(r, n, create_using=None):
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75 """Creates a full r-ary tree of n vertices.
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76
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77 Sometimes called a k-ary, n-ary, or m-ary tree.
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78 "... all non-leaf vertices have exactly r children and all levels
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79 are full except for some rightmost position of the bottom level
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80 (if a leaf at the bottom level is missing, then so are all of the
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81 leaves to its right." [1]_
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82
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83 Parameters
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84 ----------
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85 r : int
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86 branching factor of the tree
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87 n : int
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88 Number of nodes in the tree
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89 create_using : NetworkX graph constructor, optional (default=nx.Graph)
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90 Graph type to create. If graph instance, then cleared before populated.
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91
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92 Returns
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93 -------
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94 G : networkx Graph
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95 An r-ary tree with n nodes
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96
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97 References
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98 ----------
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99 .. [1] An introduction to data structures and algorithms,
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100 James Andrew Storer, Birkhauser Boston 2001, (page 225).
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101 """
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102 G = empty_graph(n, create_using)
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103 G.add_edges_from(_tree_edges(n, r))
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104 return G
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105
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106
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107 def balanced_tree(r, h, create_using=None):
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108 """Returns the perfectly balanced `r`-ary tree of height `h`.
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109
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110 Parameters
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111 ----------
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112 r : int
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113 Branching factor of the tree; each node will have `r`
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114 children.
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115
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116 h : int
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117 Height of the tree.
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118
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119 create_using : NetworkX graph constructor, optional (default=nx.Graph)
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120 Graph type to create. If graph instance, then cleared before populated.
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121
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122 Returns
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123 -------
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124 G : NetworkX graph
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125 A balanced `r`-ary tree of height `h`.
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126
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127 Notes
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128 -----
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129 This is the rooted tree where all leaves are at distance `h` from
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130 the root. The root has degree `r` and all other internal nodes
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131 have degree `r + 1`.
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132
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133 Node labels are integers, starting from zero.
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134
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135 A balanced tree is also known as a *complete r-ary tree*.
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136
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137 """
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138 # The number of nodes in the balanced tree is `1 + r + ... + r^h`,
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139 # which is computed by using the closed-form formula for a geometric
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140 # sum with ratio `r`. In the special case that `r` is 1, the number
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141 # of nodes is simply `h + 1` (since the tree is actually a path
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142 # graph).
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143 if r == 1:
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144 n = h + 1
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145 else:
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146 # This must be an integer if both `r` and `h` are integers. If
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147 # they are not, we force integer division anyway.
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148 n = (1 - r ** (h + 1)) // (1 - r)
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149 return full_rary_tree(r, n, create_using=create_using)
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150
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151
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152 def barbell_graph(m1, m2, create_using=None):
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153 """Returns the Barbell Graph: two complete graphs connected by a path.
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154
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155 For $m1 > 1$ and $m2 >= 0$.
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156
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157 Two identical complete graphs $K_{m1}$ form the left and right bells,
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158 and are connected by a path $P_{m2}$.
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159
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160 The `2*m1+m2` nodes are numbered
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161 `0, ..., m1-1` for the left barbell,
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162 `m1, ..., m1+m2-1` for the path,
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163 and `m1+m2, ..., 2*m1+m2-1` for the right barbell.
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164
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165 The 3 subgraphs are joined via the edges `(m1-1, m1)` and
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166 `(m1+m2-1, m1+m2)`. If `m2=0`, this is merely two complete
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167 graphs joined together.
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168
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169 This graph is an extremal example in David Aldous
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170 and Jim Fill's e-text on Random Walks on Graphs.
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171
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172 """
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173 if m1 < 2:
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174 raise NetworkXError(
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175 "Invalid graph description, m1 should be >=2")
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176 if m2 < 0:
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177 raise NetworkXError(
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178 "Invalid graph description, m2 should be >=0")
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179
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180 # left barbell
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181 G = complete_graph(m1, create_using)
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182 if G.is_directed():
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183 raise NetworkXError("Directed Graph not supported")
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184
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185 # connecting path
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186 G.add_nodes_from(range(m1, m1 + m2 - 1))
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187 if m2 > 1:
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188 G.add_edges_from(pairwise(range(m1, m1 + m2)))
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189 # right barbell
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190 G.add_edges_from((u, v) for u in range(m1 + m2, 2 * m1 + m2)
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191 for v in range(u + 1, 2 * m1 + m2))
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192 # connect it up
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193 G.add_edge(m1 - 1, m1)
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194 if m2 > 0:
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195 G.add_edge(m1 + m2 - 1, m1 + m2)
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196 return G
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197
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198 def binomial_tree(n):
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199 """Returns the Binomial Tree of order n.
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200
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201 The binomial tree of order 0 consists of a single vertex. A binomial tree of order k
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202 is defined recursively by linking two binomial trees of order k-1: the root of one is
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203 the leftmost child of the root of the other.
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204
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205 Parameters
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206 ----------
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207 n : int
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208 Order of the binomial tree.
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209
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210 Returns
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211 -------
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212 G : NetworkX graph
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213 A binomial tree of $2^n$ vertices and $2^n - 1$ edges.
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214
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215 """
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216 G = nx.empty_graph(1)
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217 N = 1
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218 for i in range(n):
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219 edges = [(u + N, v + N) for (u, v) in G.edges]
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220 G.add_edges_from(edges)
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221 G.add_edge(0,N)
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222 N *= 2
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223 return G
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224
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225 @nodes_or_number(0)
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226 def complete_graph(n, create_using=None):
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227 """ Return the complete graph `K_n` with n nodes.
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228
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229 Parameters
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230 ----------
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231 n : int or iterable container of nodes
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232 If n is an integer, nodes are from range(n).
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233 If n is a container of nodes, those nodes appear in the graph.
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234 create_using : NetworkX graph constructor, optional (default=nx.Graph)
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235 Graph type to create. If graph instance, then cleared before populated.
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236
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237 Examples
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238 --------
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239 >>> G = nx.complete_graph(9)
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240 >>> len(G)
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241 9
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242 >>> G.size()
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243 36
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244 >>> G = nx.complete_graph(range(11, 14))
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245 >>> list(G.nodes())
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246 [11, 12, 13]
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247 >>> G = nx.complete_graph(4, nx.DiGraph())
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248 >>> G.is_directed()
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249 True
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250
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251 """
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252 n_name, nodes = n
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253 G = empty_graph(n_name, create_using)
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254 if len(nodes) > 1:
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255 if G.is_directed():
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256 edges = itertools.permutations(nodes, 2)
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257 else:
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258 edges = itertools.combinations(nodes, 2)
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259 G.add_edges_from(edges)
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260 return G
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261
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262
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263 def circular_ladder_graph(n, create_using=None):
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264 """Returns the circular ladder graph $CL_n$ of length n.
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265
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266 $CL_n$ consists of two concentric n-cycles in which
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267 each of the n pairs of concentric nodes are joined by an edge.
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268
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269 Node labels are the integers 0 to n-1
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270
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271 """
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272 G = ladder_graph(n, create_using)
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273 G.add_edge(0, n - 1)
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274 G.add_edge(n, 2 * n - 1)
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275 return G
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276
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277
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278 def circulant_graph(n, offsets, create_using=None):
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279 """Generates the circulant graph $Ci_n(x_1, x_2, ..., x_m)$ with $n$ vertices.
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280
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281 Returns
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282 -------
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283 The graph $Ci_n(x_1, ..., x_m)$ consisting of $n$ vertices $0, ..., n-1$ such
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284 that the vertex with label $i$ is connected to the vertices labelled $(i + x)$
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285 and $(i - x)$, for all $x$ in $x_1$ up to $x_m$, with the indices taken modulo $n$.
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286
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287 Parameters
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288 ----------
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289 n : integer
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290 The number of vertices the generated graph is to contain.
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291 offsets : list of integers
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292 A list of vertex offsets, $x_1$ up to $x_m$, as described above.
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293 create_using : NetworkX graph constructor, optional (default=nx.Graph)
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294 Graph type to create. If graph instance, then cleared before populated.
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295
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296 Examples
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297 --------
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298 Many well-known graph families are subfamilies of the circulant graphs;
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299 for example, to generate the cycle graph on n points, we connect every
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300 vertex to every other at offset plus or minus one. For n = 10,
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301
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302 >>> import networkx
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303 >>> G = networkx.generators.classic.circulant_graph(10, [1])
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304 >>> edges = [
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305 ... (0, 9), (0, 1), (1, 2), (2, 3), (3, 4),
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306 ... (4, 5), (5, 6), (6, 7), (7, 8), (8, 9)]
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307 ...
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308 >>> sorted(edges) == sorted(G.edges())
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309 True
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310
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311 Similarly, we can generate the complete graph on 5 points with the set of
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312 offsets [1, 2]:
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313
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314 >>> G = networkx.generators.classic.circulant_graph(5, [1, 2])
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315 >>> edges = [
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316 ... (0, 1), (0, 2), (0, 3), (0, 4), (1, 2),
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317 ... (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)]
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318 ...
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319 >>> sorted(edges) == sorted(G.edges())
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320 True
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321
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322 """
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323 G = empty_graph(n, create_using)
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324 for i in range(n):
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325 for j in offsets:
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326 G.add_edge(i, (i - j) % n)
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327 G.add_edge(i, (i + j) % n)
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328 return G
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329
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330
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331 @nodes_or_number(0)
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332 def cycle_graph(n, create_using=None):
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333 """Returns the cycle graph $C_n$ of cyclically connected nodes.
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334
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335 $C_n$ is a path with its two end-nodes connected.
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336
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337 Parameters
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338 ----------
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339 n : int or iterable container of nodes
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340 If n is an integer, nodes are from `range(n)`.
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341 If n is a container of nodes, those nodes appear in the graph.
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342 create_using : NetworkX graph constructor, optional (default=nx.Graph)
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343 Graph type to create. If graph instance, then cleared before populated.
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344
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345 Notes
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346 -----
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347 If create_using is directed, the direction is in increasing order.
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348
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349 """
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350 n_orig, nodes = n
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351 G = empty_graph(nodes, create_using)
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352 G.add_edges_from(pairwise(nodes))
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353 G.add_edge(nodes[-1], nodes[0])
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354 return G
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355
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356
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357 def dorogovtsev_goltsev_mendes_graph(n, create_using=None):
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358 """Returns the hierarchically constructed Dorogovtsev-Goltsev-Mendes graph.
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359
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360 n is the generation.
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361 See: arXiv:/cond-mat/0112143 by Dorogovtsev, Goltsev and Mendes.
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362
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363 """
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364 G = empty_graph(0, create_using)
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365 if G.is_directed():
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366 raise NetworkXError("Directed Graph not supported")
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367 if G.is_multigraph():
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368 raise NetworkXError("Multigraph not supported")
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369
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370 G.add_edge(0, 1)
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371 if n == 0:
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372 return G
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373 new_node = 2 # next node to be added
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374 for i in range(1, n + 1): # iterate over number of generations.
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375 last_generation_edges = list(G.edges())
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376 number_of_edges_in_last_generation = len(last_generation_edges)
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377 for j in range(0, number_of_edges_in_last_generation):
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378 G.add_edge(new_node, last_generation_edges[j][0])
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379 G.add_edge(new_node, last_generation_edges[j][1])
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380 new_node += 1
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381 return G
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382
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383
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384 @nodes_or_number(0)
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385 def empty_graph(n=0, create_using=None, default=nx.Graph):
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386 """Returns the empty graph with n nodes and zero edges.
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387
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388 Parameters
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389 ----------
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390 n : int or iterable container of nodes (default = 0)
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391 If n is an integer, nodes are from `range(n)`.
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392 If n is a container of nodes, those nodes appear in the graph.
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393 create_using : Graph Instance, Constructor or None
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394 Indicator of type of graph to return.
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395 If a Graph-type instance, then clear and use it.
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396 If None, use the `default` constructor.
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397 If a constructor, call it to create an empty graph.
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398 default : Graph constructor (optional, default = nx.Graph)
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399 The constructor to use if create_using is None.
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400 If None, then nx.Graph is used.
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401 This is used when passing an unknown `create_using` value
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402 through your home-grown function to `empty_graph` and
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403 you want a default constructor other than nx.Graph.
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404
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405 Examples
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406 --------
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407 >>> G = nx.empty_graph(10)
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408 >>> G.number_of_nodes()
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409 10
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410 >>> G.number_of_edges()
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411 0
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412 >>> G = nx.empty_graph("ABC")
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413 >>> G.number_of_nodes()
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414 3
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415 >>> sorted(G)
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416 ['A', 'B', 'C']
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417
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418 Notes
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419 -----
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420 The variable create_using should be a Graph Constructor or a
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421 "graph"-like object. Constructors, e.g. `nx.Graph` or `nx.MultiGraph`
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422 will be used to create the returned graph. "graph"-like objects
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423 will be cleared (nodes and edges will be removed) and refitted as
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424 an empty "graph" with nodes specified in n. This capability
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425 is useful for specifying the class-nature of the resulting empty
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426 "graph" (i.e. Graph, DiGraph, MyWeirdGraphClass, etc.).
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427
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428 The variable create_using has three main uses:
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429 Firstly, the variable create_using can be used to create an
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430 empty digraph, multigraph, etc. For example,
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431
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432 >>> n = 10
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433 >>> G = nx.empty_graph(n, create_using=nx.DiGraph)
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434
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435 will create an empty digraph on n nodes.
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436
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437 Secondly, one can pass an existing graph (digraph, multigraph,
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438 etc.) via create_using. For example, if G is an existing graph
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439 (resp. digraph, multigraph, etc.), then empty_graph(n, create_using=G)
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440 will empty G (i.e. delete all nodes and edges using G.clear())
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441 and then add n nodes and zero edges, and return the modified graph.
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442
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443 Thirdly, when constructing your home-grown graph creation function
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444 you can use empty_graph to construct the graph by passing a user
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445 defined create_using to empty_graph. In this case, if you want the
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446 default constructor to be other than nx.Graph, specify `default`.
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447
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448 >>> def mygraph(n, create_using=None):
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449 ... G = nx.empty_graph(n, create_using, nx.MultiGraph)
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450 ... G.add_edges_from([(0, 1), (0, 1)])
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451 ... return G
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452 >>> G = mygraph(3)
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453 >>> G.is_multigraph()
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454 True
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455 >>> G = mygraph(3, nx.Graph)
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456 >>> G.is_multigraph()
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457 False
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458
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459 See also create_empty_copy(G).
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460
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461 """
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462 if create_using is None:
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463 G = default()
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464 elif hasattr(create_using, '_adj'):
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465 # create_using is a NetworkX style Graph
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466 create_using.clear()
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467 G = create_using
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468 else:
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469 # try create_using as constructor
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470 G = create_using()
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471
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472 n_name, nodes = n
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473 G.add_nodes_from(nodes)
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474 return G
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475
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476
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477 def ladder_graph(n, create_using=None):
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478 """Returns the Ladder graph of length n.
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479
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480 This is two paths of n nodes, with
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481 each pair connected by a single edge.
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482
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483 Node labels are the integers 0 to 2*n - 1.
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484
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485 """
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486 G = empty_graph(2 * n, create_using)
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487 if G.is_directed():
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488 raise NetworkXError("Directed Graph not supported")
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489 G.add_edges_from(pairwise(range(n)))
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490 G.add_edges_from(pairwise(range(n, 2 * n)))
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491 G.add_edges_from((v, v + n) for v in range(n))
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492 return G
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493
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494
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495 @nodes_or_number([0, 1])
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496 def lollipop_graph(m, n, create_using=None):
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497 """Returns the Lollipop Graph; `K_m` connected to `P_n`.
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498
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499 This is the Barbell Graph without the right barbell.
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500
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501 Parameters
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502 ----------
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503 m, n : int or iterable container of nodes (default = 0)
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504 If an integer, nodes are from `range(m)` and `range(m,m+n)`.
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505 If a container, the entries are the coordinate of the node.
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506
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507 The nodes for m appear in the complete graph $K_m$ and the nodes
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508 for n appear in the path $P_n$
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509 create_using : NetworkX graph constructor, optional (default=nx.Graph)
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510 Graph type to create. If graph instance, then cleared before populated.
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511
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512 Notes
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513 -----
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514 The 2 subgraphs are joined via an edge (m-1, m).
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diff changeset
515 If n=0, this is merely a complete graph.
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516
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517 (This graph is an extremal example in David Aldous and Jim
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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diff changeset
518 Fill's etext on Random Walks on Graphs.)
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diff changeset
519
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520 """
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diff changeset
521 m, m_nodes = m
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diff changeset
522 n, n_nodes = n
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diff changeset
523 M = len(m_nodes)
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diff changeset
524 N = len(n_nodes)
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parents:
diff changeset
525 if isinstance(m, int):
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diff changeset
526 n_nodes = [len(m_nodes) + i for i in n_nodes]
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parents:
diff changeset
527 if M < 2:
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diff changeset
528 raise NetworkXError(
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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diff changeset
529 "Invalid graph description, m should be >=2")
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parents:
diff changeset
530 if N < 0:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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parents:
diff changeset
531 raise NetworkXError(
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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diff changeset
532 "Invalid graph description, n should be >=0")
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diff changeset
533
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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534 # the ball
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535 G = complete_graph(m_nodes, create_using)
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diff changeset
536 if G.is_directed():
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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537 raise NetworkXError("Directed Graph not supported")
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
538 # the stick
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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diff changeset
539 G.add_nodes_from(n_nodes)
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diff changeset
540 if N > 1:
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541 G.add_edges_from(pairwise(n_nodes))
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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542 # connect ball to stick
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543 if M > 0 and N > 0:
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diff changeset
544 G.add_edge(m_nodes[-1], n_nodes[0])
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545 return G
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546
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547
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548 def null_graph(create_using=None):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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549 """Returns the Null graph with no nodes or edges.
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diff changeset
550
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diff changeset
551 See empty_graph for the use of create_using.
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552
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553 """
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guerler
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554 G = empty_graph(0, create_using)
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diff changeset
555 return G
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diff changeset
556
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diff changeset
557
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558 @nodes_or_number(0)
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diff changeset
559 def path_graph(n, create_using=None):
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560 """Returns the Path graph `P_n` of linearly connected nodes.
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561
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562 Parameters
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563 ----------
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diff changeset
564 n : int or iterable
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565 If an integer, node labels are 0 to n with center 0.
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diff changeset
566 If an iterable of nodes, the center is the first.
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567 create_using : NetworkX graph constructor, optional (default=nx.Graph)
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diff changeset
568 Graph type to create. If graph instance, then cleared before populated.
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diff changeset
569
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570 """
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571 n_name, nodes = n
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572 G = empty_graph(nodes, create_using)
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diff changeset
573 G.add_edges_from(pairwise(nodes))
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diff changeset
574 return G
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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parents:
diff changeset
575
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diff changeset
576
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diff changeset
577 @nodes_or_number(0)
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diff changeset
578 def star_graph(n, create_using=None):
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579 """ Return the star graph
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580
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diff changeset
581 The star graph consists of one center node connected to n outer nodes.
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diff changeset
582
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583 Parameters
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diff changeset
584 ----------
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diff changeset
585 n : int or iterable
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diff changeset
586 If an integer, node labels are 0 to n with center 0.
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diff changeset
587 If an iterable of nodes, the center is the first.
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diff changeset
588 create_using : NetworkX graph constructor, optional (default=nx.Graph)
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diff changeset
589 Graph type to create. If graph instance, then cleared before populated.
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diff changeset
590
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diff changeset
591 Notes
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diff changeset
592 -----
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593 The graph has n+1 nodes for integer n.
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594 So star_graph(3) is the same as star_graph(range(4)).
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diff changeset
595 """
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diff changeset
596 n_name, nodes = n
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diff changeset
597 if isinstance(n_name, int):
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diff changeset
598 nodes = nodes + [n_name] # there should be n+1 nodes
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599 first = nodes[0]
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600 G = empty_graph(nodes, create_using)
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diff changeset
601 if G.is_directed():
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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602 raise NetworkXError("Directed Graph not supported")
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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diff changeset
603 G.add_edges_from((first, v) for v in nodes[1:])
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guerler
parents:
diff changeset
604 return G
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guerler
parents:
diff changeset
605
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diff changeset
606
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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diff changeset
607 def trivial_graph(create_using=None):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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diff changeset
608 """ Return the Trivial graph with one node (with label 0) and no edges.
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guerler
parents:
diff changeset
609
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diff changeset
610 """
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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diff changeset
611 G = empty_graph(1, create_using)
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parents:
diff changeset
612 return G
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
613
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
614
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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parents:
diff changeset
615 def turan_graph(n, r):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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diff changeset
616 r""" Return the Turan Graph
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diff changeset
617
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diff changeset
618 The Turan Graph is a complete multipartite graph on $n$ vertices
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diff changeset
619 with $r$ disjoint subsets. It is the graph with the edges for any graph with
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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parents:
diff changeset
620 $n$ vertices and $r$ disjoint subsets.
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diff changeset
621
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622 Given $n$ and $r$, we generate a complete multipartite graph with
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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parents:
diff changeset
623 $r-(n \mod r)$ partitions of size $n/r$, rounded down, and
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
624 $n \mod r$ partitions of size $n/r+1$, rounded down.
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guerler
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diff changeset
625
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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diff changeset
626 Parameters
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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diff changeset
627 ----------
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diff changeset
628 n : int
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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parents:
diff changeset
629 The number of vertices.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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diff changeset
630 r : int
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
631 The number of partitions.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
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diff changeset
632 Must be less than or equal to n.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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parents:
diff changeset
633
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diff changeset
634 Notes
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diff changeset
635 -----
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diff changeset
636 Must satisfy $1 <= r <= n$.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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parents:
diff changeset
637 The graph has $(r-1)(n^2)/(2r)$ edges, rounded down.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
638 """
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
639
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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parents:
diff changeset
640 if not 1 <= r <= n:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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parents:
diff changeset
641 raise NetworkXError("Must satisfy 1 <= r <= n")
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guerler
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diff changeset
642
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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diff changeset
643 partitions = [n // r] * (r - (n % r)) + [n // r + 1] * (n % r)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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parents:
diff changeset
644 G = complete_multipartite_graph(*partitions)
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guerler
parents:
diff changeset
645 return G
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
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646
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647
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648 @nodes_or_number(0)
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649 def wheel_graph(n, create_using=None):
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650 """ Return the wheel graph
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651
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652 The wheel graph consists of a hub node connected to a cycle of (n-1) nodes.
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653
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654 Parameters
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655 ----------
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656 n : int or iterable
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657 If an integer, node labels are 0 to n with center 0.
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658 If an iterable of nodes, the center is the first.
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659 create_using : NetworkX graph constructor, optional (default=nx.Graph)
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660 Graph type to create. If graph instance, then cleared before populated.
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661
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662 Node labels are the integers 0 to n - 1.
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663 """
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664 n_name, nodes = n
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665 if n_name == 0:
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666 G = empty_graph(0, create_using)
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667 return G
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668 G = star_graph(nodes, create_using)
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669 if len(G) > 2:
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670 G.add_edges_from(pairwise(nodes[1:]))
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671 G.add_edge(nodes[-1], nodes[1])
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672 return G
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673
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674
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675 def complete_multipartite_graph(*subset_sizes):
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676 """Returns the complete multipartite graph with the specified subset sizes.
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677
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678 Parameters
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679 ----------
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680 subset_sizes : tuple of integers or tuple of node iterables
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681 The arguments can either all be integer number of nodes or they
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682 can all be iterables of nodes. If integers, they represent the
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683 number of vertices in each subset of the multipartite graph.
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684 If iterables, each is used to create the nodes for that subset.
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685 The length of subset_sizes is the number of subsets.
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686
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687 Returns
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688 -------
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689 G : NetworkX Graph
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690 Returns the complete multipartite graph with the specified subsets.
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691
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692 For each node, the node attribute 'subset' is an integer
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693 indicating which subset contains the node.
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694
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695 Examples
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696 --------
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697 Creating a complete tripartite graph, with subsets of one, two, and three
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698 vertices, respectively.
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699
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700 >>> import networkx as nx
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701 >>> G = nx.complete_multipartite_graph(1, 2, 3)
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702 >>> [G.nodes[u]['subset'] for u in G]
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703 [0, 1, 1, 2, 2, 2]
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704 >>> list(G.edges(0))
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705 [(0, 1), (0, 2), (0, 3), (0, 4), (0, 5)]
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706 >>> list(G.edges(2))
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707 [(2, 0), (2, 3), (2, 4), (2, 5)]
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708 >>> list(G.edges(4))
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709 [(4, 0), (4, 1), (4, 2)]
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710
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711 >>> G = nx.complete_multipartite_graph('a', 'bc', 'def')
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712 >>> [G.nodes[u]['subset'] for u in sorted(G)]
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713 [0, 1, 1, 2, 2, 2]
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714
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715 Notes
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716 -----
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717 This function generalizes several other graph generator functions.
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718
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719 - If no subset sizes are given, this returns the null graph.
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720 - If a single subset size `n` is given, this returns the empty graph on
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721 `n` nodes.
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722 - If two subset sizes `m` and `n` are given, this returns the complete
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723 bipartite graph on `m + n` nodes.
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724 - If subset sizes `1` and `n` are given, this returns the star graph on
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725 `n + 1` nodes.
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726
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727 See also
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728 --------
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729 complete_bipartite_graph
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730 """
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731 # The complete multipartite graph is an undirected simple graph.
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732 G = Graph()
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733
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734 if len(subset_sizes) == 0:
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735 return G
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736
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737 # set up subsets of nodes
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738 try:
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739 extents = pairwise(accumulate((0,) + subset_sizes))
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740 subsets = [range(start, end) for start, end in extents]
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741 except TypeError:
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742 subsets = subset_sizes
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743
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744 # add nodes with subset attribute
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745 # while checking that ints are not mixed with iterables
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746 try:
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747 for (i, subset) in enumerate(subsets):
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748 G.add_nodes_from(subset, subset=i)
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749 except TypeError:
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750 raise NetworkXError("Arguments must be all ints or all iterables")
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751
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752 # Across subsets, all vertices should be adjacent.
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753 # We can use itertools.combinations() because undirected.
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754 for subset1, subset2 in itertools.combinations(subsets, 2):
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755 G.add_edges_from(itertools.product(subset1, subset2))
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756 return G