Identifying symmetries and predicting cluster synchronization in complex networks

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 computational cost is linear in $N$. 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.

5 pages, 3 figures (Communicated to Physical Review Letters)

References in corpus (6)

• Cooperative Game Theory Approaches for Network Partitioning
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• Network synchronization of groups
• Symmetries and Cluster Synchronization in Multilayer Networks
• Stable Chimeras and Independently Synchronizable Clusters
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Cited by in corpus (5)

• Eigenvector-based analysis of cluster synchronization in general complex networks of coupled chaotic oscillators
• Fundamental interactions in self-organized critical dynamics on higher-order networks
• Cluster Synchronization via Graph Laplacian Eigenvectors
• Controlling centrality: The Inverse ranking problem for spectral centralities of complex networks
• Simultaneous global and local clustering in multiplex networks with covariate information