Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/generators/atlas.py @ 0:4f3585e2f14b draft default tip
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author | shellac |
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date | Mon, 22 Mar 2021 18:12:50 +0000 |
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1 """ |
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2 Generators for the small graph atlas. |
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3 """ |
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4 import gzip |
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5 from itertools import islice |
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6 import os |
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7 import os.path |
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8 |
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9 import networkx as nx |
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10 |
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11 __all__ = ["graph_atlas", "graph_atlas_g"] |
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12 |
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13 #: The total number of graphs in the atlas. |
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14 #: |
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15 #: The graphs are labeled starting from 0 and extending to (but not |
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16 #: including) this number. |
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17 NUM_GRAPHS = 1253 |
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18 |
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19 #: The absolute path representing the directory containing this file. |
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20 THIS_DIR = os.path.dirname(os.path.abspath(__file__)) |
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21 |
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22 #: The path to the data file containing the graph edge lists. |
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23 #: |
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24 #: This is the absolute filename of the gzipped text file containing the |
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25 #: edge list for each graph in the atlas. The file contains one entry |
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26 #: per graph in the atlas, in sequential order, starting from graph |
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27 #: number 0 and extending through graph number 1252 (see |
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28 #: :data:`NUM_GRAPHS`). Each entry looks like |
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29 #: |
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30 #: .. sourcecode:: text |
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31 #: |
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32 #: GRAPH 6 |
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33 #: NODES 3 |
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34 #: 0 1 |
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35 #: 0 2 |
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36 #: |
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37 #: where the first two lines are the graph's index in the atlas and the |
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38 #: number of nodes in the graph, and the remaining lines are the edge |
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39 #: list. |
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40 #: |
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41 #: This file was generated from a Python list of graphs via code like |
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42 #: the following:: |
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43 #: |
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44 #: import gzip |
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45 #: from networkx.generators.atlas import graph_atlas_g |
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46 #: from networkx.readwrite.edgelist import write_edgelist |
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47 #: |
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48 #: with gzip.open('atlas.dat.gz', 'wb') as f: |
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49 #: for i, G in enumerate(graph_atlas_g()): |
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50 #: f.write(bytes(f'GRAPH {i}\n', encoding='utf-8')) |
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51 #: f.write(bytes(f'NODES {len(G)}\n', encoding='utf-8')) |
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52 #: write_edgelist(G, f, data=False) |
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53 #: |
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54 ATLAS_FILE = os.path.join(THIS_DIR, "atlas.dat.gz") |
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55 |
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56 |
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57 def _generate_graphs(): |
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58 """Sequentially read the file containing the edge list data for the |
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59 graphs in the atlas and generate the graphs one at a time. |
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60 |
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61 This function reads the file given in :data:`.ATLAS_FILE`. |
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62 |
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63 """ |
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64 with gzip.open(ATLAS_FILE, "rb") as f: |
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65 line = f.readline() |
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66 while line and line.startswith(b"GRAPH"): |
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67 # The first two lines of each entry tell us the index of the |
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68 # graph in the list and the number of nodes in the graph. |
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69 # They look like this: |
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70 # |
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71 # GRAPH 3 |
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72 # NODES 2 |
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73 # |
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74 graph_index = int(line[6:].rstrip()) |
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75 line = f.readline() |
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76 num_nodes = int(line[6:].rstrip()) |
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77 # The remaining lines contain the edge list, until the next |
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78 # GRAPH line (or until the end of the file). |
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79 edgelist = [] |
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80 line = f.readline() |
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81 while line and not line.startswith(b"GRAPH"): |
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82 edgelist.append(line.rstrip()) |
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83 line = f.readline() |
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84 G = nx.Graph() |
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85 G.name = f"G{graph_index}" |
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86 G.add_nodes_from(range(num_nodes)) |
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87 G.add_edges_from(tuple(map(int, e.split())) for e in edgelist) |
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88 yield G |
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89 |
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90 |
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91 def graph_atlas(i): |
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92 """Returns graph number `i` from the Graph Atlas. |
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93 |
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94 For more information, see :func:`.graph_atlas_g`. |
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95 |
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96 Parameters |
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97 ---------- |
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98 i : int |
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99 The index of the graph from the atlas to get. The graph at index |
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100 0 is assumed to be the null graph. |
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101 |
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102 Returns |
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103 ------- |
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104 list |
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105 A list of :class:`~networkx.Graph` objects, the one at index *i* |
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106 corresponding to the graph *i* in the Graph Atlas. |
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107 |
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108 See also |
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109 -------- |
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110 graph_atlas_g |
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111 |
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112 Notes |
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113 ----- |
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114 The time required by this function increases linearly with the |
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115 argument `i`, since it reads a large file sequentially in order to |
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116 generate the graph [1]_. |
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117 |
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118 References |
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119 ---------- |
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120 .. [1] Ronald C. Read and Robin J. Wilson, *An Atlas of Graphs*. |
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121 Oxford University Press, 1998. |
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122 |
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123 """ |
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124 if not (0 <= i < NUM_GRAPHS): |
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125 raise ValueError(f"index must be between 0 and {NUM_GRAPHS}") |
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126 return next(islice(_generate_graphs(), i, None)) |
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127 |
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128 |
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129 def graph_atlas_g(): |
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130 """Returns the list of all graphs with up to seven nodes named in the |
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131 Graph Atlas. |
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132 |
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133 The graphs are listed in increasing order by |
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134 |
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135 1. number of nodes, |
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136 2. number of edges, |
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137 3. degree sequence (for example 111223 < 112222), |
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138 4. number of automorphisms, |
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139 |
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140 in that order, with three exceptions as described in the *Notes* |
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141 section below. This causes the list to correspond with the index of |
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142 the graphs in the Graph Atlas [atlas]_, with the first graph, |
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143 ``G[0]``, being the null graph. |
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144 |
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145 Returns |
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146 ------- |
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147 list |
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148 A list of :class:`~networkx.Graph` objects, the one at index *i* |
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149 corresponding to the graph *i* in the Graph Atlas. |
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150 |
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151 See also |
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152 -------- |
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153 graph_atlas |
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154 |
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155 Notes |
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156 ----- |
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157 This function may be expensive in both time and space, since it |
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158 reads a large file sequentially in order to populate the list. |
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159 |
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160 Although the NetworkX atlas functions match the order of graphs |
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161 given in the "Atlas of Graphs" book, there are (at least) three |
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162 errors in the ordering described in the book. The following three |
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163 pairs of nodes violate the lexicographically nondecreasing sorted |
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164 degree sequence rule: |
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165 |
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166 - graphs 55 and 56 with degree sequences 001111 and 000112, |
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167 - graphs 1007 and 1008 with degree sequences 3333444 and 3333336, |
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168 - graphs 1012 and 1213 with degree sequences 1244555 and 1244456. |
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169 |
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170 References |
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171 ---------- |
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172 .. [atlas] Ronald C. Read and Robin J. Wilson, |
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173 *An Atlas of Graphs*. |
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174 Oxford University Press, 1998. |
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175 |
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176 """ |
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177 return list(_generate_graphs()) |