The canonical permutation brings every isomorphic graphs into the same (labeled) graph.
canonical_permutation( graph, colors, sh = c("fm", "f", "fs", "fl", "flm", "fsm") )
The input graph, treated as undirected.
The colors of the individual vertices of the graph; only
vertices having the same color are allowed to match each other in an
automorphism. When omitted, igraph uses the
Type of the heuristics to use for the BLISS algorithm. See details for possible values.
canonical_permutation() computes a permutation which brings the graph
into canonical form, as defined by the BLISS algorithm. All isomorphic
graphs have the same canonical form.
See the paper below for the details about BLISS. This and more information is available at http://www.tcs.hut.fi/Software/bliss/index.html.
The possible values for the
sh argument are:
First non-singleton cell.
First largest non-singleton cell.
First smallest non-singleton cell.
First maximally non-trivially connectec non-singleton cell.
Largest maximally non-trivially connected non-singleton cell.
Smallest maximally non-trivially connected non-singleton cell.
See the paper in references for details about these.
A list with the following members:
The canonical permutation which takes the input graph into canonical form. A numeric vector, the first element is the new label of vertex 0, the second element for vertex 1, etc.
Some information about the BLISS computation. A named list with the following members:
Tommi Junttila for BLISS, Gabor Csardi email@example.com for the igraph and R interfaces.
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.
permute() to apply a permutation to a graph,
graph.isomorphic() for deciding graph isomorphism, possibly
based on canonical labels.
Other graph isomorphism:
## Calculate the canonical form of a random graph g1 <- sample_gnm(10, 20) cp1 <- canonical_permutation(g1) cf1 <- permute(g1, cp1$labeling) ## Do the same with a random permutation of it g2 <- permute(g1, sample(vcount(g1))) cp2 <- canonical_permutation(g2) cf2 <- permute(g2, cp2$labeling) ## Check that they are the same el1 <- as_edgelist(cf1) el2 <- as_edgelist(cf2) el1 <- el1[order(el1[, 1], el1[, 2]), ] el2 <- el2[order(el2[, 1], el2[, 2]), ] all(el1 == el2)
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