Canonical permutation of a graph
The canonical permutation brings every isomorphic graphs into the same (labeled) graph.
- The input graph, treated as undirected.
- 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
The possible values for the
sh argument are:
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
See the paper in references for details about these.
- A list with the following members:
labeling The canonical parmutation 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. info Some information about the BLISS computation. A named list with the following members: [object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
- Canonical permutation
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.
## Calculate the canonical form of a random graph g1 <- erdos.renyi.game(10, 20, type="gnm") cp1 <- canonical.permutation(g1) cf1 <- permute.vertices(g1, cp1$labeling) ## Do the same with a random permutation of it g2 <- permute.vertices(g1, sample(vcount(g1))) cp2 <- canonical.permutation(g2) cf2 <- permute.vertices(g2, cp2$labeling) ## Check that they are the same el1 <- get.edgelist(cf1) el2 <- get.edgelist(cf2) el1 <- el1[ order(el1[,1], el1[,2]), ] el2 <- el2[ order(el2[,1], el2[,2]), ] all(el1 == el2)