Localization of multilayer networks by the optimized single-layer rewiring

TL;DR

This paper investigates how the principal eigenvector of multilayer networks can be localized or delocalized through edge rewiring, revealing the sensitivity of localization to structural changes and its implications for real-world networks.

Contribution

It introduces an optimization-based rewiring method to control PEV localization in multilayer networks, highlighting the impact of single-edge modifications.

Findings

Rewiring one layer suffices to induce high localization.

Single edge rewiring can cause complete delocalization.

Localization behavior aligns with real-world social and biological networks.

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.