98 lines
2.7 KiB
Python
98 lines
2.7 KiB
Python
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#!/usr/bin/env python
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"""
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=====
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Atlas
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=====
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Atlas of all graphs of 6 nodes or less.
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"""
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# Author: Aric Hagberg (hagberg@lanl.gov)
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# Copyright (C) 2004-2019 by
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# Aric Hagberg <hagberg@lanl.gov>
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# Dan Schult <dschult@colgate.edu>
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# Pieter Swart <swart@lanl.gov>
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# All rights reserved.
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# BSD license.
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import random
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try:
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import pygraphviz
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from networkx.drawing.nx_agraph import graphviz_layout
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except ImportError:
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try:
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import pydot
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from networkx.drawing.nx_pydot import graphviz_layout
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except ImportError:
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raise ImportError("This example needs Graphviz and either "
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"PyGraphviz or pydot.")
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import matplotlib.pyplot as plt
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import networkx as nx
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from networkx.algorithms.isomorphism.isomorph import graph_could_be_isomorphic as isomorphic
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from networkx.generators.atlas import graph_atlas_g
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def atlas6():
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""" Return the atlas of all connected graphs of 6 nodes or less.
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Attempt to check for isomorphisms and remove.
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"""
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Atlas = graph_atlas_g()[0:208] # 208
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# remove isolated nodes, only connected graphs are left
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U = nx.Graph() # graph for union of all graphs in atlas
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for G in Atlas:
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zerodegree = [n for n in G if G.degree(n) == 0]
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for n in zerodegree:
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G.remove_node(n)
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U = nx.disjoint_union(U, G)
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# iterator of graphs of all connected components
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C = (U.subgraph(c) for c in nx.connected_components(U))
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UU = nx.Graph()
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# do quick isomorphic-like check, not a true isomorphism checker
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nlist = [] # list of nonisomorphic graphs
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for G in C:
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# check against all nonisomorphic graphs so far
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if not iso(G, nlist):
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nlist.append(G)
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UU = nx.disjoint_union(UU, G) # union the nonisomorphic graphs
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return UU
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def iso(G1, glist):
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"""Quick and dirty nonisomorphism checker used to check isomorphisms."""
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for G2 in glist:
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if isomorphic(G1, G2):
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return True
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return False
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if __name__ == '__main__':
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G = atlas6()
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print("graph has %d nodes with %d edges"
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% (nx.number_of_nodes(G), nx.number_of_edges(G)))
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print(nx.number_connected_components(G), "connected components")
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plt.figure(1, figsize=(8, 8))
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# layout graphs with positions using graphviz neato
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pos = graphviz_layout(G, prog="neato")
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# color nodes the same in each connected subgraph
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C = (G.subgraph(c) for c in nx.connected_components(G))
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for g in C:
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c = [random.random()] * nx.number_of_nodes(g) # random color...
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nx.draw(g,
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pos,
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node_size=40,
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node_color=c,
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vmin=0.0,
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vmax=1.0,
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with_labels=False
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)
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plt.show()
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