pymnet.get_complete_invariant

pymnet.get_complete_invariant(net, allowed_aspects='all', backend='auto')

Returns a value that is a complete invariant under multilayer network isomorphism.

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.

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:

complete_invariantobject

The returned object is a complete invariant under the specified multilayer network isomorphism. That is, any two objects returned by this function are the same exactly when the two networks are isomorphic. Note that the isomorphism types (allowed_aspects) need to match in order for the comparison to be valid. The actual object can depend on the backend that was used.

References

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