canonical_permutation  R Documentation 
The canonical permutation brings every isomorphic graphs into the same (labeled) graph.
canonical_permutation(
graph,
colors,
sh = c("fm", "f", "fs", "fl", "flm", "fsm")
)
graph 
The input graph, treated as undirected. 
colors 
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 
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 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. 
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.
Other graph isomorphism:
count_isomorphisms()
,
count_subgraph_isomorphisms()
,
graph_from_isomorphism_class()
,
isomorphic()
,
isomorphism_class()
,
isomorphisms()
,
subgraph_isomorphic()
,
subgraph_isomorphisms()
## 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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