def _assert_fractionally_isomorphic(G=None, H=None, algorithm='cep'):
if G is None:
G = graph_from_file('data/graph1.txt')
if H is None:
H = graph_from_file('data/graph2.txt')
are_isomorphic, S = are_fractionally_isomorphic(G, H, algorithm=algorithm)
assert are_isomorphic
if algorithm == 'cep':
partition1, partition2 = S
assert is_valid_partition(G, partition1)
assert is_valid_partition(H, partition2)
assert is_partition_equitable(G, partition1)
assert is_partition_equitable(H, partition2)
assert are_common_partitions(G, partition1, H, partition2)
else:
assert verify_isomorphism(G, H, S)
def _cep_solver(G, H):
"""Solves the fractional graph isomorphism problem by comparing the
coarsest equitable partitions of G and H.
Returns a two-tuple whose left element is a Boolean representing whether
the two graphs have a common coarsest partition and whose right element is
the pair of partitions of the given graphs (in the same order as the inputs
are given). If the left element is ``False``, the right element is
``None``, since there is no witness that the graphs are fractionally
isomorphic.
"""
partition1 = coarsest_equitable_partition(G)
partition2 = coarsest_equitable_partition(H)
result = are_common_partitions(G, partition1, H, partition2)
witness = (partition1, partition2) if result else None
return result, witness
def _cep_solver(G, H):
"""Solves the fractional graph isomorphism problem by comparing the
coarsest equitable partitions of G and H.
Returns a two-tuple whose left element is a Boolean representing whether
the two graphs have a common coarsest partition and whose right element is
the pair of partitions of the given graphs (in the same order as the inputs
are given). If the left element is ``False``, the right element is
``None``, since there is no witness that the graphs are fractionally
isomorphic.
"""
partition1 = coarsest_equitable_partition(G)
partition2 = coarsest_equitable_partition(H)
result = are_common_partitions(G, partition1, H, partition2)
witness = (partition1, partition2) if result else None
return result, witness
