Number of automorphismsSource:
Calculate the number of automorphisms of a graph, i.e. the number of isomorphisms to itself.
count_automorphisms(graph, colors, sh = c("fm", "f", "fs", "fl", "flm", "fsm"))
The input graph, it is treated as undirected.
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
colorattribute of the vertices, or, if there is no such vertex attribute, it simply assumes that all vertices have the same color. Pass NULL explicitly if the graph has a
colorvertex attribute but you do not want to use it.
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.
A named list with the following members:
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.
The number of nodes in the search tree.
The number of leaf nodes in the search tree.
Number of bad nodes.
Number of canrep updates.
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. If you need the
automorphisms themselves, use
automorphism_group() to obtain
a compact representation of the automorphism group.
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.
## 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) count_automorphisms(g) #> $nof_nodes #>  6 #> #> $nof_leaf_nodes #>  4 #> #> $nof_bad_nodes #>  0 #> #> $nof_canupdates #>  1 #> #> $max_level #>  2 #> #> $group_size #>  "20" #> ## A full graph has n! automorphisms; however, we restrict the vertex ## matching by colors, leading to only 4 automorphisms g <- make_full_graph(4) count_automorphisms(g, colors = c(1, 2, 1, 2)) #> $nof_nodes #>  5 #> #> $nof_leaf_nodes #>  3 #> #> $nof_bad_nodes #>  0 #> #> $nof_canupdates #>  1 #> #> $max_level #>  2 #> #> $group_size #>  "4" #>