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Identifying symmetries and predicting cluster synchronization in complex networks

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

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.

Suggested Citation

  • Khanra, Pitambar & Ghosh, Subrata & Alfaro-Bittner, Karin & Kundu, Prosenjit & Boccaletti, Stefano & Hens, Chittaranjan & Pal, Pinaki, 2022. "Identifying symmetries and predicting cluster synchronization in complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    • Handle: RePEc:eee:chsofr:v:155:y:2022:i:c:s0960077921010572
    DOI: 10.1016/j.chaos.2021.111703
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    References listed on IDEAS

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    1. Louis M. Pecora & Francesco Sorrentino & Aaron M. Hagerstrom & Thomas E. Murphy & Rajarshi Roy, 2014. "Cluster synchronization and isolated desynchronization in complex networks with symmetries," Nature Communications, Nature, vol. 5(1), pages 1-8, September.
    2. Fabio Rossa & Louis Pecora & Karen Blaha & Afroza Shirin & Isaac Klickstein & Francesco Sorrentino, 2020. "Symmetries and cluster synchronization in multilayer networks," Nature Communications, Nature, vol. 11(1), pages 1-17, December.
    3. Pradhan, Priodyuti & C.U., Angeliya & Jalan, Sarika, 2020. "Principal eigenvector localization and centrality in networks: Revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    4. Khanra, Pitambar & Pal, Pinaki, 2021. "Explosive synchronization in multilayer networks through partial adaptation," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
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