Identifying symmetries and predicting cluster synchronization in complex networks

Pitambar Khanra, Subrata Ghosh, Karin Alfaro-Bittner, Prosenjit Kundu, Stefano Boccaletti, Chittaranjan Hens, Pinaki Pal

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

Symmetries in a network connectivity regulate how the graph's functioning organizes into clustered states. Classical methods for tracing the symmetry group of a network require very high computational costs, and therefore they are of hard, or even impossible, execution for large sized graphs. We here unveil that there is a direct connection between the elements of the eigen-vector centrality and the clusters of a network. This gives a fresh framework for cluster analysis in undirected and connected graphs, whose time complexity is of O(N2). We show that the cluster identification is in perfect agreement with symmetry based analyses, and it allows predicting the sequence of synchronized clusters which form before the eventual occurrence of global synchronization.

Original languageEnglish
Article number111703
JournalChaos, Solitons and Fractals
Volume155
DOIs
StatePublished - Feb 2022
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2021 Elsevier Ltd

Keywords

  • 05.45.Gg
  • 05.45.Xt
  • 85.25.Cp
  • 87.19.Lm

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