Provides a Python implementation of the ISMAGS algorithm.
It is capable of finding (subgraph) isomorphisms between two graphs, taking the symmetry of the subgraph into account. In most cases the VF2 algorithm is faster (at least on small graphs) than this implementation, but in some cases there is an exponential number of isomorphisms that are symmetrically equivalent. In that case, the ISMAGS algorithm will provide only one solution per symmetry group.
>>> petersen = nx.petersen_graph()
>>> ismags = nx.isomorphism.ISMAGS(petersen, petersen)
>>> isomorphisms = list(ismags.isomorphisms_iter(symmetry=False))
>>> len(isomorphisms)
120
>>> isomorphisms = list(ismags.isomorphisms_iter(symmetry=True))
>>> answer = [{0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7, 8: 8, 9: 9}]
>>> answer == isomorphisms
True
In addition, this implementation also provides an interface to find the largest common induced subgraph between any two graphs, again taking symmetry into account. Given graph
and :None:None:`subgraph` the algorithm will remove nodes from the :None:None:`subgraph` until :None:None:`subgraph` is isomorphic to a subgraph of graph
. Since only the symmetry of :None:None:`subgraph` is taken into account it is worth thinking about how you provide your graphs:
>>> graph1 = nx.path_graph(4)
>>> graph2 = nx.star_graph(3)
>>> ismags = nx.isomorphism.ISMAGS(graph1, graph2)
>>> ismags.is_isomorphic()
False
>>> largest_common_subgraph = list(ismags.largest_common_subgraph())
>>> answer = [{1: 0, 0: 1, 2: 2}, {2: 0, 1: 1, 3: 2}]
>>> answer == largest_common_subgraph
True
>>> ismags2 = nx.isomorphism.ISMAGS(graph2, graph1)
>>> largest_common_subgraph = list(ismags2.largest_common_subgraph())
>>> answer = [
... {1: 0, 0: 1, 2: 2},
... {1: 0, 0: 1, 3: 2},
... {2: 0, 0: 1, 1: 2},
... {2: 0, 0: 1, 3: 2},
... {3: 0, 0: 1, 1: 2},
... {3: 0, 0: 1, 2: 2},
... ]
>>> answer == largest_common_subgraph
True
However, when not taking symmetry into account, it doesn't matter:
>>> largest_common_subgraph = list(ismags.largest_common_subgraph(symmetry=False))
>>> answer = [
... {1: 0, 0: 1, 2: 2},
... {1: 0, 2: 1, 0: 2},
... {2: 0, 1: 1, 3: 2},
... {2: 0, 3: 1, 1: 2},
... {1: 0, 0: 1, 2: 3},
... {1: 0, 2: 1, 0: 3},
... {2: 0, 1: 1, 3: 3},
... {2: 0, 3: 1, 1: 3},
... {1: 0, 0: 2, 2: 3},
... {1: 0, 2: 2, 0: 3},
... {2: 0, 1: 2, 3: 3},
... {2: 0, 3: 2, 1: 3},
... ]
>>> answer == largest_common_subgraph
True
>>> largest_common_subgraph = list(ismags2.largest_common_subgraph(symmetry=False))
>>> answer = [
... {1: 0, 0: 1, 2: 2},
... {1: 0, 0: 1, 3: 2},
... {2: 0, 0: 1, 1: 2},
... {2: 0, 0: 1, 3: 2},
... {3: 0, 0: 1, 1: 2},
... {3: 0, 0: 1, 2: 2},
... {1: 1, 0: 2, 2: 3},
... {1: 1, 0: 2, 3: 3},
... {2: 1, 0: 2, 1: 3},
... {2: 1, 0: 2, 3: 3},
... {3: 1, 0: 2, 1: 3},
... {3: 1, 0: 2, 2: 3},
... ]
>>> answer == largest_common_subgraph
True
The current implementation works for undirected graphs only. The algorithm in general should work for directed graphs as well though.
Node keys for both provided graphs need to be fully orderable as well as hashable.
Node and edge equality is assumed to be transitive: if A is equal to B, and B is equal to C, then A is equal to C.
Provides a Python implementation of the ISMAGS algorithm.
It is capable of finding (subgraph) isomorphisms between two graphs, taking the symmetry of the subgraph into account. In most cases the VF2 algorithm is faster (at least on small graphs) than this implementation, but in some cases there is an exponential number of isomorphisms that are symmetrically equivalent. In that case, the ISMAGS algorithm will provide only one solution per symmetry group.
>>> petersen = nx.petersen_graph()
>>> ismags = nx.isomorphism.ISMAGS(petersen, petersen)
>>> isomorphisms = list(ismags.isomorphisms_iter(symmetry=False))
>>> len(isomorphisms)
120
>>> isomorphisms = list(ismags.isomorphisms_iter(symmetry=True))
>>> answer = [{0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7, 8: 8, 9: 9}]
>>> answer == isomorphisms
True
In addition, this implementation also provides an interface to find the largest common induced subgraph between any two graphs, again taking symmetry into account. Given graph
and :None:None:`subgraph` the algorithm will remove nodes from the :None:None:`subgraph` until :None:None:`subgraph` is isomorphic to a subgraph of graph
. Since only the symmetry of :None:None:`subgraph` is taken into account it is worth thinking about how you provide your graphs:
>>> graph1 = nx.path_graph(4)
>>> graph2 = nx.star_graph(3)
>>> ismags = nx.isomorphism.ISMAGS(graph1, graph2)
>>> ismags.is_isomorphic()
False
>>> largest_common_subgraph = list(ismags.largest_common_subgraph())
>>> answer = [{1: 0, 0: 1, 2: 2}, {2: 0, 1: 1, 3: 2}]
>>> answer == largest_common_subgraph
True
>>> ismags2 = nx.isomorphism.ISMAGS(graph2, graph1)
>>> largest_common_subgraph = list(ismags2.largest_common_subgraph())
>>> answer = [
... {1: 0, 0: 1, 2: 2},
... {1: 0, 0: 1, 3: 2},
... {2: 0, 0: 1, 1: 2},
... {2: 0, 0: 1, 3: 2},
... {3: 0, 0: 1, 1: 2},
... {3: 0, 0: 1, 2: 2},
... ]
>>> answer == largest_common_subgraph
True
However, when not taking symmetry into account, it doesn't matter:
>>> largest_common_subgraph = list(ismags.largest_common_subgraph(symmetry=False))
>>> answer = [
... {1: 0, 0: 1, 2: 2},
... {1: 0, 2: 1, 0: 2},
... {2: 0, 1: 1, 3: 2},
... {2: 0, 3: 1, 1: 2},
... {1: 0, 0: 1, 2: 3},
... {1: 0, 2: 1, 0: 3},
... {2: 0, 1: 1, 3: 3},
... {2: 0, 3: 1, 1: 3},
... {1: 0, 0: 2, 2: 3},
... {1: 0, 2: 2, 0: 3},
... {2: 0, 1: 2, 3: 3},
... {2: 0, 3: 2, 1: 3},
... ]
>>> answer == largest_common_subgraph
True
>>> largest_common_subgraph = list(ismags2.largest_common_subgraph(symmetry=False))
>>> answer = [
... {1: 0, 0: 1, 2: 2},
... {1: 0, 0: 1, 3: 2},
... {2: 0, 0: 1, 1: 2},
... {2: 0, 0: 1, 3: 2},
... {3: 0, 0: 1, 1: 2},
... {3: 0, 0: 1, 2: 2},
... {1: 1, 0: 2, 2: 3},
... {1: 1, 0: 2, 3: 3},
... {2: 1, 0: 2, 1: 3},
... {2: 1, 0: 2, 3: 3},
... {3: 1, 0: 2, 1: 3},
... {3: 1, 0: 2, 2: 3},
... ]
>>> answer == largest_common_subgraph
True
The current implementation works for undirected graphs only. The algorithm in general should work for directed graphs as well though.
Node keys for both provided graphs need to be fully orderable as well as hashable.
Node and edge equality is assumed to be transitive: if A is equal to B, and B is equal to C, then A is equal to C.
<Unimplemented 'footnote' '.. [1] M. Houbraken, S. Demeyer, T. Michoel, P. Audenaert, D. Colle,\n M. Pickavet, "The Index-Based Subgraph Matching Algorithm with General\n Symmetries (ISMAGS): Exploiting Symmetry for Faster Subgraph\n Enumeration", PLoS One 9(5): e97896, 2014.\n https://doi.org/10.1371/journal.pone.0097896'><Unimplemented 'footnote' '.. [2] https://en.wikipedia.org/wiki/Maximum_common_induced_subgraph'>
Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.
Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)
SVG is more flexible but power hungry; and does not scale well to 50 + nodes.
All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them