Atlas of all graphs of 6 nodes or less.



graph has 779 nodes with 1073 edges
137 connected components

# Author: Aric Hagberg (

#    Copyright (C) 2004-2019 by
#    Aric Hagberg <>
#    Dan Schult <>
#    Pieter Swart <>
#    All rights reserved.
#    BSD license.

import random

    import pygraphviz
    from networkx.drawing.nx_agraph import graphviz_layout
except ImportError:
        import pydot
        from networkx.drawing.nx_pydot import graphviz_layout
    except ImportError:
        raise ImportError("This example needs Graphviz and either "
                          "PyGraphviz or pydot.")

import matplotlib.pyplot as plt

import networkx as nx
from networkx.algorithms.isomorphism.isomorph import graph_could_be_isomorphic as isomorphic
from networkx.generators.atlas import graph_atlas_g

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

    Atlas = 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 == 0]
        for n in zerodegree:
        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):
            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__':
    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")

    plt.figure(1, figsize=(8, 8))
    # layout graphs with positions using graphviz neato
    pos = 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...

Total running time of the script: ( 0 minutes 4.914 seconds)

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