  Calculating a product of multiple graphs has been studied in mathematics,
engineering, computer science, and more recently in network science,
particularly in the context of multilayer networks. One of the important
questions to be addressed in this area is how to characterize spectral
properties of a product graph using those of its factor graphs. While several
such characterizations have already been obtained analytically (mostly for
adjacency spectra), characterization of Laplacian spectra of direct product and
strong product graphs has remained an open problem. Here we develop practical
methods to estimate Laplacian spectra of direct and strong product graphs from
spectral properties of their factor graphs using a few heuristic assumptions.
Numerical experiments showed that the proposed methods produced reasonable
estimation with percentage errors confined within a +/-10% range for most
eigenvalues.
