igraph (version 1.2.4)

automorphisms: Number of automorphisms

Description

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

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: ‘f’: first non-singleton cell, ‘fl’: first largest non-singleton cell, ‘fs’: first smallest non-singleton cell, ‘fm’: first maximally non-trivially connected non-singleton cell, ‘flm’: first largest maximally non-trivially connected non-singleton cell, ‘fsm’: first smallest maximally non-trivially connected non-singleton cell.

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.

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 http://www.tcs.hut.fi/Software/bliss/index.html.

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

canonical_permutation, permute

Examples

# NOT RUN {
## 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)
# }