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.

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.

# 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)
# }