# canonical.permutation

##### Canonical permutation of a graph

The canonical permutation brings every isomorphic graphs into the same (labeled) graphs.

- Keywords
- graphs

##### Usage

`canonical.permutation(graph, sh="fm")`

##### Arguments

- graph
- The input graph, treated as undirected.
- sh
- Type of the heuristics to use for the BLISS algorithm. See details for possible values.

##### Details

`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:

- f

##### Value

- 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: - nof\_nodes

- nof_leaf_nodes
{The number of leaf nodes in the search tree.}- nof_bad_nodes
{Number of bad nodes.}- nof_canupdates
{Number of canrep updates.}- max_level
{Maximum level.}- group_size
{The size of the automorphism group of the input graph, as a string. This number is exact if igraph was compiled with the GMP library, and approximate otherwise.}

##### concept

- Canonical permutation
- BLISS

##### References

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.

##### See Also

`permute.vertices`

to apply a permutation to a
graph, `graph.isomorphic`

for deciding graph isomorphism,
possibly based on canonical labels.

##### Examples

```
## 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$labeling)
## Do the same with a random permutation of it
g2 <- permute.vertices(g1, sample(vcount(g1))-1)
cp2 <- canonical.permutation(g2)
cf2 <- permute.vertices(g2, cp2$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)
```

*Documentation reproduced from package igraph, version 0.5.5-3, License: GPL (>= 2)*