Estimation of Laplacian spectra of direct and strong product graphs

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)160-170
Number of pages11
JournalDiscrete Applied Mathematics
Volume205
DOIs
Publication statusPublished - 2016
Externally publishedYes

Fingerprint

Strong Product
Laplacian Spectrum
Product Graph
Direct Product
Factor Graph
Spectral Properties
Computer science
Multilayers
Adjacency
Percentage
Multilayer
Open Problems
Computer Science
Numerical Experiment
Heuristics
Engineering
Eigenvalue
Experiments
Graph in graph theory
Estimate

Keywords

  • Direct product
  • Laplacian spectrum
  • Multilayer network
  • Product graph
  • Strong product

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

Estimation of Laplacian spectra of direct and strong product graphs. / Sayama, Hiroki.

In: Discrete Applied Mathematics, Vol. 205, 2016, p. 160-170.

Research output: Contribution to journalArticle

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