Graph product multilayer networks: Spectral properties and applications

Hiroki Sayama*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)430-447
Number of pages18
JournalJournal of Complex Networks
Issue number3
Publication statusPublished - 2018 Jul 1
Externally publishedYes


  • Degree/adjacency/Laplacian spectra
  • Epidemic thresholds
  • Graph product
  • Multilayer networks
  • Propagation
  • Self-similar networks

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Management Science and Operations Research
  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics


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