Identifying symmetries and predicting cluster synchronization in complex networks
arXiv:2102.06957 · doi:10.1016/j.chaos.2021.111703
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 . 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.
arXiv comment5 pages, 3 figures (Communicated to Physical Review Letters)
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- Simultaneous global and local clustering in multiplex networks with covariate information