Decide if two graphs are isomorphic

`isomorphic(graph1, graph2, method = c("auto", "direct", "vf2", "bliss"), ...)`is_isomorphic_to(graph1, graph2, method = c("auto", "direct", "vf2", "bliss"),
...)

graph1

The first graph.

graph2

The second graph.

method

The method to use. Possible values: ‘auto’, ‘direct’, ‘vf2’, ‘bliss’. See their details below.

...

Additional arguments, passed to the various methods.

Logical scalar, `TRUE`

if the graphs are isomorphic.

It tries to select the appropriate method based on the two graphs. This is the algorithm it uses:

If the two graphs do not agree on their order and size (i.e. number of vertices and edges), then return

`FALSE`

.If the graphs have three or four vertices, then the ‘direct’ method is used.

If the graphs are directed, then the ‘vf2’ method is used.

Otherwise the ‘bliss’ method is used.

This method only works on graphs with three or four vertices, and it is based on a pre-calculated and stored table. It does not have any extra arguments.

This method uses the VF2 algorithm by Cordella, Foggia et al., see references below. It supports vertex and edge colors and have the following extra arguments:

- vertex.color1, vertex.color2
Optional integer vectors giving the colors of the vertices for colored graph isomorphism. If they are not given, but the graph has a “color” vertex attribute, then it will be used. If you want to ignore these attributes, then supply

`NULL`

for both of these arguments. See also examples below.- edge.color1, edge.color2
Optional integer vectors giving the colors of the edges for edge-colored (sub)graph isomorphism. If they are not given, but the graph has a “color” edge attribute, then it will be used. If you want to ignore these attributes, then supply

`NULL`

for both of these arguments.

Uses the BLISS algorithm by Junttila and Kaski, and it works for
undirected graphs. For both graphs the
`canonical_permutation`

and then the `permute`

function is called to transfer them into canonical form; finally the
canonical forms are compared.
Extra arguments:

- sh1
Character constant, the heuristics to use in the BLISS algorithm, for

`graph1`

. See the`sh`

argument of`canonical_permutation`

for possible values.- sh2
Character constant, the heuristics to use in the BLISS algorithm, for

`graph2`

. See the`sh`

argument of`canonical_permutation`

for possible values.

`sh1`

and `sh2`

default to ‘fm’.

Tommi Junttila and Petteri Kaski: Engineering an Efficient Canonical
Labeling Tool for Large and Sparse Graphs, *Proceedings of the
Ninth Workshop on Algorithm Engineering and Experiments and the Fourth
Workshop on Analytic Algorithms and Combinatorics.* 2007.

LP Cordella, P Foggia, C Sansone, and M Vento: An improved algorithm
for matching large graphs, *Proc. of the 3rd IAPR TC-15 Workshop
on Graphbased Representations in Pattern Recognition*, 149--159, 2001.

Other graph isomorphism: `count_isomorphisms`

,
`graph.count.isomorphisms.vf2`

;
`count_subgraph_isomorphisms`

,
`graph.count.subisomorphisms.vf2`

;
`graph.get.isomorphisms.vf2`

,
`isomorphisms`

;
`graph.get.subisomorphisms.vf2`

,
`subgraph_isomorphisms`

;
`graph.isoclass`

,
`graph.isoclass.subgraph`

,
`isomorphism_class`

;
`graph.isocreate`

,
`graph_from_isomorphism_class`

;
`graph.subisomorphic.lad`

,
`graph.subisomorphic.vf2`

,
`is_subgraph_isomorphic_to`

,
`subgraph_isomorphic`

# NOT RUN { # create some non-isomorphic graphs g1 <- graph_from_isomorphism_class(3, 10) g2 <- graph_from_isomorphism_class(3, 11) isomorphic(g1, g2) # create two isomorphic graphs, by permuting the vertices of the first g1 <- barabasi.game(30, m=2, directed=FALSE) g2 <- permute(g1, sample(vcount(g1))) # should be TRUE isomorphic(g1, g2) isomorphic(g1, g2, method = "bliss") isomorphic(g1, g2, method = "vf2") # colored graph isomorphism g1 <- make_ring(10) g2 <- make_ring(10) isomorphic(g1, g2) V(g1)$color <- rep(1:2, length = vcount(g1)) V(g2)$color <- rep(2:1, length = vcount(g2)) # consider colors by default count_isomorphisms(g1, g2) # ignore colors count_isomorphisms(g1, g2, vertex.color1 = NULL, vertex.color2 = NULL) # }