Localization of multilayer networks by the optimized single-layer rewiring

Abstract

We study localization properties of principal eigenvector (PEV) of multilayer networks. Starting with a multilayer network corresponding to a delocalized PEV, we rewire the network edges using an optimization technique such that the PEV of the rewired multilayer network becomes more localized. The framework allows us to scrutinize structural and spectral properties of the networks at various localization points during the rewiring process. We show that rewiring only one-layer is enough to attain a multilayer network having a highly localized PEV. Our investigation reveals that a single edge rewiring of the optimized multilayer network can lead to the complete delocalization of a highly localized PEV. This sensitivity in the localization behavior of PEV is accompanied by a pair of almost degenerate eigenvalues. This observation opens an avenue to gain a deeper insight into the origin of PEV localization of networks. Furthermore, analysis of multilayer networks constructed using real-world social and biological data show that the localization properties of these real-world multilayer networks are in good agreement with the simulation results for the model multilayer network. The study is relevant to applications that require understanding propagation of perturbation in multilayer networks.

10 pages, 8 figures

References in corpus (12)

• Power-law distributions in empirical data
• The structure and dynamics of multilayer networks
• Layer aggregation and reducibility of multilayer interconnected networks
• Efficiently Summarising Event Sequences with Rich Interleaving Patterns
• MuxViz: A Tool for Multilayer Analysis and Visualization of Networks
• Synchronization in networks with multiple interaction layers
• Optimal percolation on multiplex networks
• Relating Topological Determinants of Complex Networks to Their Spectral Properties: Structural and Dynamical Effects
• Optimization of synchronizability in multiplex networks by rewiring one layer
• Optimized evolution of networks for principal eigenvector localization
• Is repulsion good for the health of Chimeras?
• Localization in random bipartite graphs: numerical and empirical study

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• Wheel graph strategy for PEV localization of networks
• Explosive Synchronization in Multilayer Dynamically Dissimilar Networks
• Random Matrix Analysis of Multiplex Networks
• Network construction: A learning framework through localizing principal eigenvector