# automorphisms

From igraph v1.0.0
by Gabor Csardi

##### Number of automorphisms

Calculate the number of automorphisms of a graph, i.e. the number of isomorphisms to itself.

- Keywords
- graphs

##### Usage

`automorphisms(graph, sh = "fm")`

##### Arguments

- graph
- The input graph, it is treated as undirected.
- sh
- The splitting heuristics for the BLISS algorithm. Possible values
are:
: first non-singleton cell,`f`

: first largest non-singleton cell,`fl`

: first smallest non-sing`fs`

##### Details

An automorphism of a graph is a permutation of its vertices which brings the graph into itself.

This function calculates the number of automorphism of a graph using the
BLISS algorithm. See also the BLISS homepage at

##### Value

- A named list with the following members:
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. nof_nodes The number of nodes in the search tree. 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.

##### 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

##### Examples

```
## A ring has n*2 automorphisms, you can "turn" it by 0-9 vertices
## and each of these graphs can be "flipped"
g <- make_ring(10)
automorphisms(g)
```

*Documentation reproduced from package igraph, version 1.0.0, License: GPL (>= 2)*

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