atlas.py :  » Network » NetworkX » networkx-1.1 » networkx » generators » Python Open Source

"""
Generators for the small graph atlas.


See
"An Atlas of Graphs" by Ronald C. Read and Robin J. Wilson,
Oxford University Press, 1998.

Because of its size, this module is not imported by default.

"""
#    Copyright (C) 2004-2008 by 
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
#    All rights reserved.
#    BSD license.
__author__ = """Pieter Swart (swart@lanl.gov)"""
 
__all__ = ['graph_atlas_g']

from networkx.generators.small import make_small_graph

def graph_atlas_g():
    """
    Return the list [G0,G1,...,G1252] of graphs as named in the Graph Atlas.
    G0,G1,...,G1252 are all graphs with up to 7 nodes.

    The graphs are listed:
      1. in increasing order of number of nodes;
      2. for a fixed number of nodes,
         in increasing order of the number of edges;
      3. for fixed numbers of nodes and edges,
         in increasing order of the degree sequence,
         for example 111223 < 112222;
      4. for fixed degree sequence, in increasing number of automorphisms.

    Note that indexing is set up so that for
    GAG=graph_atlas_g(), then
    G123=GAG[123] and G[0]=empty_graph(0)

    """

    descr_list=[
     ['edgelist', 'G0', 0, []],
     ['edgelist', 'G1', 1, []],
     ['edgelist', 'G2', 2, []],
     ['edgelist', 'G3', 2, [[1, 2]]],
     ['edgelist', 'G4', 3, []],
     ['edgelist', 'G5', 3, [[2, 3]]],
     ['edgelist', 'G6', 3, [[1, 2], [1, 3]]],
     ['edgelist', 'G7', 3, [[1, 2], [1, 3], [2, 3]]],
     ['edgelist', 'G8', 4, []],
     ['edgelist', 'G9', 4, [[4, 3]]],
     ['edgelist', 'G10', 4, [[4, 3], [4, 2]]],
     ['edgelist', 'G11', 4, [[1, 2], [4, 3]]],
     ['edgelist', 'G12', 4, [[4, 3], [2, 3], [4, 2]]],
     ['edgelist', 'G13', 4, [[4, 1], [4, 2], [4, 3]]],
     ['edgelist', 'G14', 4, [[1, 2], [2, 3], [1, 4]]],
     ['edgelist', 'G15', 4, [[4, 3], [2, 3], [4, 2], [4, 1]]],
     ['edgelist', 'G16', 4, [[1, 2], [2, 3], [3, 4], [1, 4]]],
     ['edgelist', 'G17', 4, [[1, 2], [1, 3], [1, 4], [2, 3], [3, 4]]],
     ['edgelist', 'G18', 4, [[1, 2], [2, 3], [1, 3], [4, 1], [4, 2], [4, 3]]],
     ['edgelist', 'G19', 5, []],
     ['edgelist', 'G20', 5, [[5, 4]]],
     ['edgelist', 'G21', 5, [[2, 3], [1, 2]]],
     ['edgelist', 'G22', 5, [[1, 3], [5, 4]]],
     ['edgelist', 'G23', 5, [[2, 3], [1, 2], [3, 1]]],
     ['edgelist', 'G24', 5, [[5, 4], [4, 3], [4, 2]]],
     ['edgelist', 'G25', 5, [[4, 3], [5, 4], [1, 5]]],
     ['edgelist', 'G26', 5, [[2, 3], [1, 2], [5, 4]]],
     ['edgelist', 'G27', 5, [[5, 4], [2, 3], [4, 2], [4, 3]]],
     ['edgelist', 'G28', 5, [[1, 4], [2, 1], [3, 2], [4, 3]]],
     ['edgelist', 'G29', 5, [[5, 4], [5, 1], [5, 2], [5, 3]]],
     ['edgelist', 'G30', 5, [[5, 1], [4, 2], [5, 4], [4, 3]]],
     ['edgelist', 'G31', 5, [[3, 4], [2, 3], [1, 2], [5, 1]]],
     ['edgelist', 'G32', 5, [[2, 3], [1, 2], [3, 1], [5, 4]]],
     ['edgelist', 'G33', 5, [[1, 4], [3, 1], [4, 3], [2, 1], [3, 2]]],
     ['edgelist', 'G34', 5, [[5, 3], [5, 4], [3, 4], [5, 2], [5, 1]]],
     ['edgelist', 'G35', 5, [[1, 2], [2, 3], [3, 4], [1, 5], [1, 3]]],
     ['edgelist', 'G36', 5, [[5, 1], [2, 3], [5, 4], [4, 3], [4, 2]]],
     ['edgelist', 'G37', 5, [[2, 1], [5, 2], [3, 5], [4, 3], [2, 4]]],
     ['edgelist', 'G38', 5, [[1, 2], [2, 3], [3, 4], [4, 5], [1, 5]]],
     ['edgelist', 'G39', 5, [[2, 1], [5, 2], [5, 1], [1, 4], [2, 4], [4, 5]]],
     ['edgelist', 'G40', 5, [[2, 1], [5, 2], [3, 5], [4, 3], [2, 4], [3, 2]]],
     ['edgelist', 'G41', 5, [[2, 1], [5, 2], [3, 5], [4, 3], [2, 4], [4, 5]]],
     ['edgelist', 'G42', 5, [[1, 2], [5, 4], [3, 4], [5, 3], [5, 1], [5, 2]]],
     ['edgelist', 'G43', 5, [[1, 5], [4, 1], [5, 4], [3, 4], [2, 3], [1, 2]]],
     ['edgelist', 'G44', 5, [[3, 2], [1, 3], [4, 1], [2, 4], [5, 2], [1, 5]]],
     ['edgelist',
      'G45',
      5,
      [[5, 1], [2, 3], [5, 4], [4, 3], [4, 2], [5, 2], [3, 5]]],
     ['edgelist',
      'G46',
      5,
      [[5, 2], [3, 5], [4, 3], [2, 4], [4, 5], [1, 4], [5, 1]]],
     ['edgelist',
      'G47',
      5,
      [[1, 2], [2, 3], [3, 4], [4, 5], [1, 5], [2, 4], [5, 2]]],
     ['edgelist',
      'G48',
      5,
      [[3, 2], [1, 3], [4, 1], [2, 4], [5, 2], [1, 5], [3, 5]]],
     ['edgelist',
      'G49',
      5,
      [[2, 1], [5, 2], [3, 5], [4, 3], [2, 4], [5, 1], [4, 5], [1, 4]]],
     ['edgelist',
      'G50',
      5,
      [[1, 2], [2, 3], [3, 4], [1, 4], [5, 1], [5, 2], [5, 3], [5, 4]]],
     ['edgelist',
      'G51',
      5,
      [[1, 2], [4, 5], [1, 4], [1, 5], [2, 3], [2, 4], [2, 5], [3, 4], [3, 5]]],
     ['edgelist',
      'G52',
      5,
      [[1, 2],
       [1, 3],
       [1, 4],
       [1, 5],
       [2, 3],
       [2, 4],
       [2, 5],
       [3, 4],
       [3, 5],
       [4, 5]]],
     ['edgelist', 'G53', 6, []],
     ['edgelist', 'G54', 6, [[6, 5]]],
     ['edgelist', 'G55', 6, [[1, 4], [6, 5]]],
     ['edgelist', 'G56', 6, [[2, 4], [2, 3]]],
     ['edgelist', 'G57', 6, [[2, 4], [3, 2], [4, 3]]],
     ['edgelist', 'G58', 6, [[1, 4], [6, 1], [5, 1]]],
     ['edgelist', 'G59', 6, [[5, 4], [6, 5], [1, 6]]],
     ['edgelist', 'G60', 6, [[5, 4], [6, 2], [6, 3]]],
     ['edgelist', 'G61', 6, [[2, 3], [4, 1], [6, 5]]],
     ['edgelist', 'G62', 6, [[1, 4], [5, 1], [6, 5], [1, 6]]],
     ['edgelist', 'G63', 6, [[4, 1], [6, 4], [5, 6], [1, 5]]],
     ['edgelist', 'G64', 6, [[6, 2], [6, 4], [6, 3], [1, 6]]],
     ['edgelist', 'G65', 6, [[5, 4], [4, 2], [5, 1], [4, 3]]],
     ['edgelist', 'G66', 6, [[1, 3], [2, 4], [3, 2], [6, 4]]],
     ['edgelist', 'G67', 6, [[2, 4], [3, 2], [4, 3], [1, 6]]],
     ['edgelist', 'G68', 6, [[2, 3], [1, 4], [6, 1], [5, 1]]],
     ['edgelist', 'G69', 6, [[5, 6], [2, 3], [1, 6], [4, 5]]],
     ['edgelist', 'G70', 6, [[1, 3], [5, 1], [4, 2], [6, 4]]],
     ['edgelist', 'G71', 6, [[4, 1], [6, 4], [5, 6], [1, 5], [6, 1]]],
     ['edgelist', 'G72', 6, [[6, 4], [4, 2], [4, 3], [5, 4], [5, 6]]],
     ['edgelist', 'G73', 6, [[6, 4], [6, 5], [3, 4], [4, 5], [1, 5]]],
     ['edgelist', 'G74', 6, [[5, 4], [2, 3], [5, 1], [4, 3], [4, 2]]],
     ['edgelist', 'G75', 6, [[2, 5], [4, 5], [5, 1], [3, 2], [4, 3]]],
     ['edgelist', 'G76', 6, [[1, 2], [2, 3], [3, 4], [4, 5], [1, 5]]],
     ['edgelist', 'G77', 6, [[6, 4], [6, 5], [6, 1], [6, 2], [6, 3]]],
     ['edgelist', 'G78', 6, [[2, 5], [6, 2], [2, 1], [3, 2], [3, 4]]],
     ['edgelist', 'G79', 6, [[1, 2], [4, 5], [1, 3], [4, 1], [6, 4]]],
     ['edgelist', 'G80', 6, [[2, 1], [3, 2], [3, 5], [2, 4], [6, 4]]],
     ['edgelist', 'G81', 6, [[5, 4], [1, 6], [5, 1], [4, 3], [4, 2]]],
     ['edgelist', 'G82', 6, [[2, 3], [1, 2], [5, 6], [2, 4], [3, 4]]],
     ['edgelist', 'G83', 6, [[1, 2], [1, 6], [3, 4], [4, 5], [5, 6]]],
     ['edgelist', 'G84', 6, [[5, 4], [6, 2], [6, 3], [1, 4], [5, 1]]],
     ['edgelist', 'G85', 6, [[2, 3], [4, 1], [6, 4], [5, 6], [1, 5]]],
     ['edgelist', 'G86', 6, [[1, 4], [6, 1], [5, 6], [4, 5], [6, 4], [5, 1]]],
     ['edgelist', 'G87', 6, [[2, 5], [3, 5], [5, 1], [3, 4], [4, 2], [4, 5]]],
     ['edgelist', 'G88', 6, [[2, 5], [3, 5], [5, 1], [3, 2], [4, 2], [3, 4]]],
     ['edgelist', 'G89', 6, [[3, 1], [6, 5], [5, 4], [6, 4], [5, 1], [3, 5]]],
     ['edgelist', 'G90', 6, [[4, 3], [5, 4], [1, 5], [2, 1], [3, 2], [1, 4]]],
     ['edgelist', 'G91', 6, [[5, 2], [4, 2], [5, 3], [4, 3], [3, 1], [2, 1]]],
     ['edgelist', 'G92', 6, [[6, 3], [6, 4], [6, 5], [4, 5], [6, 2], [6, 1]]],
     ['edgelist', 'G93', 6, [[5, 4], [5, 3], [5, 1], [2, 5], [4, 1], [6, 4]]],
     ['edgelist', 'G94', 6, [[5, 4], [4, 6], [6, 5], [6, 2], [4, 3], [5, 1]]],
     ['edgelist', 'G95', 6, [[5, 3], [2, 3], [5, 4], [5, 2], [5, 1], [1, 6]]],
     ['edgelist', 'G96', 6, [[2, 3], [4, 2], [1, 4], [3, 1], [5, 1], [6, 1]]],
     ['edgelist', 'G97', 6, [[3, 1], [5, 3], [2, 5], [3, 2], [4, 2], [6, 4]]],
     ['edgelist', 'G98', 6, [[2, 3], [4, 2], [1, 4], [3, 1], [5, 1], [6, 4]]],
     ['edgelist', 'G99', 6, [[6, 4], [3, 6], [3, 1], [5, 3], [5, 4], [4, 2]]],
     ['edgelist', 'G100', 6, [[1, 3], [4, 5], [2, 1], [6, 4], [5, 6], [4, 1]]],
     ['edgelist', 'G101', 6, [[2, 3], [4, 1], [6, 4], [5, 6], [1, 5], [6, 1]]],
     ['edgelist', 'G102', 6, [[5, 4], [2, 3], [5, 1], [4, 3], [4, 2], [6, 1]]],
     ['edgelist', 'G103', 6, [[2, 5], [3, 5], [5, 1], [1, 6], [4, 2], [3, 4]]],
     ['edgelist', 'G104', 6, [[1, 2], [2, 3], [3, 4], [4, 5], [1, 5], [2, 6]]],
     ['edgelist', 'G105', 6, [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [1, 6]]],
     ['edgelist', 'G106', 6, [[2, 4], [3, 2], [4, 3], [1, 5], [6, 1], [5, 6]]],
     ['edgelist',
      'G107',
      6,
      [[1, 2], [2, 3], [1, 3], [4, 1], [4, 2], [4, 3], [1, 6]]],
     ['edgelist',
      'G108',
      6,
      [[2, 5], [3, 5], [3, 2], [4, 2], [3, 4], [3, 1], [1, 2]]],
     ['edgelist',
      'G109',
      6,
      [[1, 2], [2, 3], [3, 4], [4, 5], [1, 5], [2, 4], [5, 2]]],
     ['edgelist',
      'G110',
      6,
      [[1, 2], [4, 3], [1, 3], [4, 1], [4, 2], [6, 2], [6, 3]]],
     ['edgelist',
      'G111',
      6,
      [[2, 5], [3, 5], [3, 4], [1, 5], [4, 2], [5, 6], [4, 5]]],
     ['edgelist',
      'G112',
      6,
      [[2, 1], [5, 2], [3, 5], [4, 3], [6, 2], [3, 6], [2, 3]]],
     ['edgelist',
      'G113',
      6,
      [[1, 5], [3, 1], [2, 3], [4, 2], [6, 4], [4, 1], [3, 4]]],
     ['edgelist',
      'G114',
      6,
      [[2, 5], [3, 5], [3, 4], [3, 2], [4, 2], [5, 6], [1, 5]]],
     ['edgelist',
      'G115',
      6,
      [[2, 1], [5, 2], [3, 5], [4, 3], [6, 2], [3, 6], [5, 6]]],
     ['edgelist',
      'G116',
      6,
      [[1, 2], [2, 3], [1, 3], [4, 1], [4, 2], [4, 3], [6, 5]]],
     ['edgelist',
      'G117',
      6,
      [[1, 6], [5, 1], [6, 5], [1, 3], [4, 1], [4, 3], [1, 2]]],
     ['edgelist',
      'G118',
      6,
      [[1, 2], [2, 3], [3, 4], [4, 5], [1, 5], [2, 6], [5, 2]]],
     ['edgelist',
      'G119',
      6,
      [[1, 2], [5, 1], [2, 5], [1, 3], [4, 1], [4, 3], [4, 6]]],
     ['edgelist',
      'G120',
      6,
      [[2, 5], [3, 5], [5, 1], [1, 6], [4, 2], [3, 4], [4, 5]]],
     ['edgelist',
      'G121',
      6,
      [[3, 1], [4, 3], [5, 4], [6, 5], [3, 6], [2, 3], [5, 2]]],
     ['edgelist',
      'G122',
      6,
      [[2, 6], [1, 2], [5, 1], [4, 5], [3, 4], [2, 3], [1, 4]]],
     ['edgelist',
      'G123',
      6,
      [[2, 5], [3, 5], [5, 1], [1, 6], [4, 2], [3, 4], [3, 2]]],
     ['edgelist',
      'G124',
      6,
      [[1, 2], [2, 3], [3, 4], [4, 5], [1, 5], [1, 3], [6, 2]]],
     ['edgelist',
      'G125',
      6,
      [[3, 1], [5, 2], [2, 3], [6, 5], [3, 6], [4, 2], [6, 4]]],
     ['edgelist',
      'G126',
      6,
      [[6, 1], [4, 6], [3, 4], [1, 3], [2, 4], [5, 2], [4, 5]]],
     ['edgelist',
      'G127',
      6,
      [[2, 4], [3, 2], [1, 3], [6, 1], [5, 6], [4, 5], [3, 4]]],
     ['edgelist',
      'G128',
      6,
      [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [1, 6], [1, 4]]],
     ['edgelist',
      'G129',
      6,
      [[5, 4], [1, 5], [2, 1], [3, 2], [4, 3], [1, 6], [6, 4]]],
     ['edgelist',
      'G130',
      6,
      [[2, 3], [1, 2], [3, 1], [4, 1], [5, 4], [6, 5], [4, 6]]],
     ['edgelist',
      'G131',
      6,
      [[1, 2], [3, 6], [1, 3], [4, 1], [4, 2], [4, 3], [3, 2], [6, 2]]],
     ['edgelist',
      'G132',
      6,
      [[1, 2], [2, 3], [3, 4], [1, 4], [5, 1], [5, 2], [5, 3], [5, 4]]],
     ['edgelist',
      'G133',
      6,
      [[1, 2], [2, 3], [1, 3], [4, 1], [4, 2], [4, 3], [6, 1], [1, 5]]],
     ['edgelist',
      'G134',
      6,
      [[2, 3], [4, 2], [1, 4], [2, 1], [3, 1], [4, 3], [6, 4], [5, 1]]],
     ['edgelist',
      'G135',
      6,
      [[1, 2], [3, 5], [1, 3], [6, 3], [4, 2], [4, 3], [3, 2], [5, 2]]],
     ['edgelist',
      'G136',
      6,
      [[1, 2], [2, 3], [3, 4], [4, 5], [1, 5], [2, 4], [5, 2], [2, 6]]],
     ['edgelist',
      'G137',
      6,
      [[1, 2], [2, 3], [3, 4], [4, 5], [1, 5], [2, 4], [5, 2], [6, 5]]],
     ['edgelist',
      'G138',
      6,
      [[1, 2], [3, 6], [1, 3], [5, 1], [4, 2], [4, 3], [3, 2], [6, 2]]],
     ['edgelist',
      'G139',
      6,
      [[1, 2], [2, 3], [3, 4], [4, 5], [1, 5], [2, 4], [5, 2], [6, 1]]],
     ['edgelist',
      'G140',
      6,
      [[1, 2], [3, 6], [1, 3], [5, 1], [4, 2], [4, 3], [4, 1], [6, 2]]],
     ['edgelist',
      'G141',
      6,
      [[3, 1], [4, 3], [5, 4], [6, 5], [3, 6], [2, 3], [5, 2], [6, 4]]],
     ['edgelist',
      'G142',
      6,
      [[1, 2], [2, 3], [1, 3], [4, 1], [4, 2], [4, 3], [1, 6], [6, 5]]],
     ['edgelist',
      'G143',
      6,
      [[1, 2], [3, 6], [1, 3], [5, 1], [4, 2], [4, 3], [6, 2], [6, 4]]],
     ['edgelist',
      'G144',
      6,
      [[2, 5], [3, 5], [3, 4], [1, 5], [4, 2], [5, 6], [1, 6], [4, 5]]],
     ['edgelist',
      'G145',
      6,
      [[1, 2], [2, 3], [3, 4], [4, 5], [1, 5], [6, 1], [6, 3], [1, 3]]],
     ['edgelist',
      'G146',
      6,
      [[2, 6], [5, 2], [1, 5], [6, 1], [3, 6], [5, 3], [4, 5], [6, 4]]],
     ['edgelist',
      'G147',
      6,
      [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [1, 6], [3, 5], [6, 3]]],
     ['edgelist',
      'G148',
      6,
      [[2, 4], [3, 2], [1, 3], [6, 1], [5, 6], [4, 5], [2, 5], [1, 2]]],
     ['edgelist',
      'G149',
      6,
      [[1, 2], [2, 3], [3, 4], [4, 5], [1, 5], [4, 1], [6, 3], [6, 1]]],
     ['edgelist',
      'G150',
      6,
      [[2, 5], [3, 5], [3, 4], [1, 5], [4, 2], [5, 6], [1, 6], [3, 2]]],
     ['edgelist',
      'G151',
      6,
      [[1, 2], [2, 3], [3, 4], [4, 5], [1, 5], [5, 6], [6, 4], [2, 6]]],
     ['edgelist',
      'G152',
      6,
      [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [1, 6], [3, 5], [6, 2]]],
     ['edgelist',
      'G153',
      6,
      [[1, 2], [2, 3], [3, 4], [4, 5], [1, 5], [2, 6], [6, 3], [6, 1]]],
     ['edgelist',
      'G154',
      6,
      [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [1, 6], [5, 2], [6, 3]]],
     ['edgelist',
      'G155',
      6,
      [[1, 2], [2, 3], [3, 4], [4, 5], [1, 5], [2, 4], [5, 2], [3, 5], [1, 4]]],
     ['edgelist',
      'G156',
      6,
      [[1, 2], [3, 6], [1, 3], [4, 1], [4, 2], [4, 3], [3, 2], [6, 2], [5, 3]]],
     ['edgelist',
      'G157',
      6,
      [[1, 2], [3, 6], [1, 3], [4, 1], [4, 2], [4, 3], [3, 2], [6, 2], [1, 5]]],
     ['edgelist',
      'G158',
      6,
      [[1, 2], [2, 3], [3, 4], [1, 4], [5, 1], [5, 2], [5, 3], [5, 4], [5, 6]]],
     ['edgelist',
      'G159',
      6,
      [[3, 1], [5, 2], [2, 3], [6, 5], [3, 6], [4, 2], [6, 4], [4, 3], [5, 4]]],
     ['edgelist',
      'G160',
      6,
      [[1, 2], [3, 6], [1, 3], [4, 1], [4, 2], [4, 3], [3, 2], [6, 2], [5, 6]]],
     ['edgelist',
      'G161',
      6,
      [[2, 6], [5, 2], [1, 5], [6, 1], [3, 6], [5, 3], [4, 5], [6, 4], [5, 6]]],
     ['edgelist',
      'G162',
      6,
      [[1, 2], [2, 3], [3, 4], [4, 5], [1, 5], [3, 6], [1, 6], [3, 1], [4, 1]]],
     ['edgelist',
      'G163',
      6,
      [[2, 4], [3, 2], [1, 3], [6, 1], [5, 6], [4, 5], [1, 5], [2, 1], [5, 2]]],
     ['edgelist',
      'G164',
      6,
      [[2, 4], [3, 2], [1, 3], [6, 1], [5, 6], [4, 5], [5, 2], [2, 1], [6, 2]]],
     ['edgelist',
      'G165',
      6,
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       [4, 7],
       [5, 6],
       [5, 7],
       [6, 7]]]]

    GAG=[]

    for i in range(1253):
        g=make_small_graph(descr_list[i])
        GAG.append(g)

    return GAG