Warning

This documents an unmaintained version of NetworkX. Please upgrade to a maintained version and see the current NetworkX documentation.

# Source code for networkx.algorithms.isomorphism.isomorph

"""
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)'])
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
__all__ = ['could_be_isomorphic',
'fast_could_be_isomorphic',
'faster_could_be_isomorphic',
'is_isomorphic']

[docs]def could_be_isomorphic(G1,G2):
"""Returns False if graphs are definitely not isomorphic.
True does NOT guarantee isomorphism.

Parameters
----------
G1, G2 : graphs
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

[docs]def fast_could_be_isomorphic(G1,G2):
"""Returns False if graphs are definitely not isomorphic.

True does NOT guarantee isomorphism.

Parameters
----------
G1, G2 : graphs
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

[docs]def faster_could_be_isomorphic(G1,G2):
"""Returns False if graphs are definitely not isomorphic.

True does NOT guarantee isomorphism.

Parameters
----------
G1, G2 : graphs
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

[docs]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: graphs
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 node_match is not specified then node attributes are not considered.

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 as inputs.

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 edge_match is
not specified then edge attributes are not considered.

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 [1]_.

Examples
--------
>>> import networkx.algorithms.isomorphism as iso

For digraphs G1 and G2, using 'weight' edge attribute (default: 1)

>>> G1 = nx.DiGraph()
>>> G2 = nx.DiGraph()
>>> 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()
>>> 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)

>>> 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

--------
numerical_node_match, numerical_edge_match, numerical_multiedge_match
categorical_node_match, categorical_edge_match, categorical_multiedge_match

References
----------
.. [1]  L. P. Cordella, P. Foggia, C. Sansone, M. Vento,
"An Improved Algorithm for Matching Large Graphs",
3rd IAPR-TC15 Workshop  on Graph-based Representations in
Pattern Recognition, Cuen, pp. 149-159, 2001.
http://amalfi.dis.unina.it/graph/db/papers/vf-algorithm.pdf
"""
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()