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"""
Graph isomorphism functions.
"""
import networkx as nx
from networkx.exception import NetworkXError
__author__ = """\n""".join(['Aric Hagberg (hagberg@lanl.gov)',
'Pieter Swart (swart@lanl.gov)',
'Christopher Ellison cellison@cse.ucdavis.edu)'])
# Copyright (C) 2004-2011 by
# Aric Hagberg <hagberg@lanl.gov>
# Dan Schult <dschult@colgate.edu>
# Pieter Swart <swart@lanl.gov>
# All rights reserved.
# BSD license.
__all__ = ['could_be_isomorphic',
'fast_could_be_isomorphic',
'faster_could_be_isomorphic',
'is_isomorphic']
def could_be_isomorphic(G1,G2):
"""Returns False if graphs are definitely not isomorphic.
True does NOT guarantee isomorphism.
Parameters
----------
G1, G2 : NetworkX graph instances
The two graphs G1 and G2 must be the same type.
Notes
-----
Checks for matching degree, triangle, and number of cliques sequences.
"""
# Check global properties
if G1.order() != G2.order(): return False
# Check local properties
d1=G1.degree()
t1=nx.triangles(G1)
c1=nx.number_of_cliques(G1)
props1=[ [d1[v], t1[v], c1[v]] for v in d1 ]
props1.sort()
d2=G2.degree()
t2=nx.triangles(G2)
c2=nx.number_of_cliques(G2)
props2=[ [d2[v], t2[v], c2[v]] for v in d2 ]
props2.sort()
if props1 != props2:
return False
# OK...
return True
graph_could_be_isomorphic=could_be_isomorphic
def fast_could_be_isomorphic(G1,G2):
"""Returns False if graphs are definitely not isomorphic.
True does NOT guarantee isomorphism.
Parameters
----------
G1, G2 : NetworkX graph instances
The two graphs G1 and G2 must be the same type.
Notes
-----
Checks for matching degree and triangle sequences.
"""
# Check global properties
if G1.order() != G2.order(): return False
# Check local properties
d1=G1.degree()
t1=nx.triangles(G1)
props1=[ [d1[v], t1[v]] for v in d1 ]
props1.sort()
d2=G2.degree()
t2=nx.triangles(G2)
props2=[ [d2[v], t2[v]] for v in d2 ]
props2.sort()
if props1 != props2: return False
# OK...
return True
fast_graph_could_be_isomorphic=fast_could_be_isomorphic
def faster_could_be_isomorphic(G1,G2):
"""Returns False if graphs are definitely not isomorphic.
True does NOT guarantee isomorphism.
Parameters
----------
G1, G2 : NetworkX graph instances
The two graphs G1 and G2 must be the same type.
Notes
-----
Checks for matching degree sequences.
"""
# Check global properties
if G1.order() != G2.order(): return False
# Check local properties
d1=list(G1.degree().values())
d1.sort()
d2=list(G2.degree().values())
d2.sort()
if d1 != d2: return False
# OK...
return True
faster_graph_could_be_isomorphic=faster_could_be_isomorphic
def is_isomorphic(G1, G2, node_match=None, edge_match=None):
"""Returns True if the graphs G1 and G2 are isomorphic and False otherwise.
Parameters
----------
G1, G2: NetworkX graph instances
The two graphs G1 and G2 must be the same type.
node_match : callable
A function that returns True if node n1 in G1 and n2 in G2
should be considered equal during the isomorphism test.
If None`, then no node attributes are considered when testing
for isomorphism.
The function will be called like:
node_match(G1.node[n1], G2.node[n2]).
That is, the function will receive the node attribute dictionaries
for n1 and n2.
edge_match : callable
A function that returns True if the edge attribute dictionary
for the pair of nodes (u1, v1) in G1 and (u2, v2) in G2 should
be considered equal during the isomorphism test. If `None`,
then no attributes are considered when testing for an
isomorphism.
The function will be called like
edge_match(G1[u1][v1], G2[u2][v2]).
That is, the function will receive the edge attribute dictionaries
of the edges under consideration.
Notes
-----
Uses the vf2 algorithm.
Works for Graph, DiGraph, MultiGraph, and MultiDiGraph.
Examples
--------
>>> import networkx as nx
>>> import networkx.algorithms.isomorphism as iso
For digraphs G1 and G2, using 'weight' edge attribute (default: 1)
>>> G1 = nx.DiGraph()
>>> G2 = nx.DiGraph()
>>> G1.add_path([1,2,3,4],weight=1)
>>> G2.add_path([10,20,30,40],weight=2)
>>> em = iso.numerical_edge_match('weight', 1)
>>> nx.is_isomorphic(G1, G2) # no weights considered
True
>>> nx.is_isomorphic(G1, G2, edge_match=em) # match weights
False
For multidigraphs G1 and G2, using 'fill' node attribute (default: '')
>>> G1 = nx.MultiDiGraph()
>>> G2 = nx.MultiDiGraph()
>>> G1.add_nodes_from([1,2,3],fill='red')
>>> G2.add_nodes_from([10,20,30,40],fill='red')
>>> G1.add_path([1,2,3,4],weight=3, linewidth=2.5)
>>> G2.add_path([10,20,30,40],weight=3)
>>> nm = iso.categorical_node_match('fill', 'red')
>>> nx.is_isomorphic(G1, G2, node_match=nm)
True
For multidigraphs G1 and G2, using 'weight' edge attribute (default: 7)
>>> G1.add_edge(1,2, weight=7)
>>> G2.add_edge(10,20)
>>> em = iso.numerical_multiedge_match('weight', 7, rtol=1e-6)
>>> nx.is_isomorphic(G1, G2, edge_match=em)
True
For multigraphs G1 and G2, using 'weight' and 'linewidth' edge attributes
with default values 7 and 2.5. Also using 'fill' node attribute with
default value 'red'.
>>> em = iso.numerical_multiedge_match(['weight', 'linewidth'], [7, 2.5])
>>> nm = iso.categorical_node_match('fill', 'red')
>>> nx.is_isomorphic(G1, G2, edge_match=em, node_match=nm)
True
See Also
--------
:mod:`vf2userfunc`, :mod:`matchelpers`
GraphMatcher, DiGraphMatcher
numerical_node_match, numerical_edge_match, numerical_multiedge_match
categorical_node_match, categorical_edge_match, categorical_multiedge_match
"""
if G1.is_directed() and G2.is_directed():
GM = nx.algorithms.isomorphism.DiGraphMatcher
elif (not G1.is_directed()) and (not G2.is_directed()):
GM = nx.algorithms.isomorphism.GraphMatcher
else:
raise NetworkXError("Graphs G1 and G2 are not of the same type.")
gm = GM(G1, G2, node_match=node_match, edge_match=edge_match)
return gm.is_isomorphic()
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