automorphism_group | R Documentation |

Compute the generating set of the automorphism group of a graph.

```
automorphism_group(
graph,
colors,
sh = c("fm", "f", "fs", "fl", "flm", "fsm"),
details = FALSE
)
```

`graph` |
The input graph, it is 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` |
The splitting heuristics for the BLISS algorithm. Possible values
are: ‘ |

`details` |
Specifies whether to provide additional details about the BLISS internals in the result. |

An automorphism of a graph is a permutation of its vertices which brings the graph into itself. The automorphisms of a graph form a group and there exists a subset of this group (i.e. a set of permutations) such that every other permutation can be expressed as a combination of these permutations. These permutations are called the generating set of the automorphism group.

This function calculates a possible generating set of the automorphism of a graph using the BLISS algorithm. See also the BLISS homepage at http://www.tcs.hut.fi/Software/bliss/index.html. The calculated generating set is not necessarily minimal, and it may depend on the splitting heuristics used by BLISS.

When `details`

is `FALSE`

, a list of vertex permutations
that form a generating set of the automorphism group of the input graph.
When `details`

is `TRUE`

, a named list with two members:

`generators` |
Returns the generators themselves |

`info` |
Additional
information about the BLISS internals. See |

Tommi Junttila (http://users.ics.aalto.fi/tjunttil/) for BLISS, Gabor Csardi csardi.gabor@gmail.com for the igraph glue code and Tamas Nepusz ntamas@gmail.com for this manual page.

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.

`canonical_permutation()`

, `permute()`

,
`count_automorphisms()`

Other graph automorphism:
`count_automorphisms()`

```
## A ring has n*2 automorphisms, and a possible generating set is one that
## "turns" the ring by one vertex to the left or right
g <- make_ring(10)
automorphism_group(g)
```

igraph documentation built on May 31, 2023, 8:26 p.m.

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