Localization of multilayer networks by optimized single-layer rewiring

We study localization properties of principal eigenvectors (PEVs) of multilayer networks (MNs). 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 MN having a highly localized PEV. Our investigation reveals that a single edge rewiring of the optimized MN can lead to the complete delocalization of a highly localized PEV. This sensitivity in the localization behavior of PEVs is accompanied with the second largest eigenvalue lying very close to the largest one. 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 shows that the localization properties of these real-world multilayer networks are in good agreement with the simulation results for the model multilayer network. This paper is relevant to applications that require understanding propagation of perturbation in multilayer networks.