Use this if you are using igraph from R
The canonical permutation brings every isomorphic graphs into the same (labeled) graph.
canonical_permutation(graph, sh = "fm")
graph 
The input graph, treated as undirected. 
sh 
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 nonsingleton cell.
First largest nonsingleton cell.
First smallest nonsingleton cell.
First maximally nontrivially connectec nonsingleton cell.
Largest maximally nontrivially connected nonsingleton cell.
Smallest maximally nontrivially connected nonsingleton cell.
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:

Tommi Junttila for BLISS, Gabor Csardi csardi.gabor@gmail.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.
## 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)