pymnet.get_automorphism_generators

pymnet.get_automorphism_generators(net, allowed_aspects='all', include_fixed=False, backend='auto')

Returns automorphism generators for the given network. The generators are permutations that can be used to construct the automorphism group of the network.

Parameters:
netMultilayerNetwork

The multilayer network.

allowed_aspectslist of ints, string

The aspects that can be permuted in this isomorphism type. Nodes are in aspect 0 by convention. Value “all” will allow all permutations, i.e., it gives the (nonpartial) node-layer isomorphism.

include_fixedbool

If True the elementary layer permutations include elements that remain unchanged.

backendstring

The program to be used for solving the graph isomorphism of the auxiliary graphs. Value “auto” will select the best available candidate. For a list of backends, see documentation of the package.

Returns:
automorphism_generatorslist of lists of dicts

Each element in the list is a permutation for a multilayer network. A permutation of a multilayer network is a list of permutations, one for each aspect. Permutation for an aspect is a dictionary where each key is mapped to the value. If include_fixed is not set true, the dictionaries do not contain elementary layers that would be mapped to themselves.

References

“Isomorphisms in Multilayer Networks”, M. Kivela & M. A. Porter, arXiv:1506.00508 [physics.soc-ph]