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Journal Article

Graph product multilayer networks: spectral properties and applications


Sayama,  Hiroki
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Sayama, H. (2018). Graph product multilayer networks: spectral properties and applications. Journal of Complex Networks, 6(3), 430-447. doi:10.1093/comnet/cnx042.

Cite as: https://hdl.handle.net/21.11116/0000-0002-095C-E
This article aims to establish theoretical foundations of graph product multilayer networks (GPMNs), a family of multilayer networks that can be obtained as a graph product of two or more factor networks. Cartesian, direct (tensor), and strong product operators are considered, and then generalized. We first describe mathematical relationships between GPMNs and their factor networks regarding their degree/strength, adjacency, and Laplacian spectra, and then show that those relationships can still hold for non-simple and generalized GPMNs. Applications of GPMNs are discussed in three areas: predicting epidemic thresholds, modelling propagation in non-trivial space and time, and analysing higher-order properties of self-similar networks. Directions of future research are also discussed.