Atlas

[source code]

#!/usr/bin/env python
"""
Atlas of all graphs of 6 nodes or less.

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

import networkx as nx
#from networkx import *
#from networkx.generators.atlas import *
from networkx.algorithms.isomorphism.isomorph import graph_could_be_isomorphic as isomorphic
import random

def atlas6():
    """ Return the atlas of all connected graphs of 6 nodes or less.
        Attempt to check for isomorphisms and remove.
    """

    Atlas=nx.graph_atlas_g()[0:208] # 208
    # remove isolated nodes, only connected graphs are left
    U=nx.Graph() # graph for union of all graphs in atlas
    for G in Atlas:
        zerodegree=[n for n in G if G.degree(n)==0]
        for n in zerodegree:
            G.remove_node(n)
        U=nx.disjoint_union(U,G)

    # list of graphs of all connected components
    C=nx.connected_component_subgraphs(U)

    UU=nx.Graph()
    # do quick isomorphic-like check, not a true isomorphism checker
    nlist=[] # list of nonisomorphic graphs
    for G in C:
        # check against all nonisomorphic graphs so far
        if not iso(G,nlist):
            nlist.append(G)
            UU=nx.disjoint_union(UU,G) # union the nonisomorphic graphs
    return UU

def iso(G1, glist):
    """Quick and dirty nonisomorphism checker used to check isomorphisms."""
    for G2 in glist:
        if isomorphic(G1,G2):
            return True
    return False


if __name__ == '__main__':

    import networkx as nx

    G=atlas6()

    print("graph has %d nodes with %d edges"\
          %(nx.number_of_nodes(G),nx.number_of_edges(G)))
    print(nx.number_connected_components(G),"connected components")


    try:
        from networkx import graphviz_layout
    except ImportError:
        raise ImportError("This example needs Graphviz and either PyGraphviz or Pydot")

    import matplotlib.pyplot as plt
    plt.figure(1,figsize=(8,8))
    # layout graphs with positions using graphviz neato
    pos=nx.graphviz_layout(G,prog="neato")
    # color nodes the same in each connected subgraph
    C=nx.connected_component_subgraphs(G)
    for g in C:
        c=[random.random()]*nx.number_of_nodes(g) # random color...
        nx.draw(g,
             pos,
             node_size=40,
             node_color=c,
             vmin=0.0,
             vmax=1.0,
             with_labels=False
             )
    plt.savefig("atlas.png",dpi=75)