Random matrix analysis of multiplex networks

We investigate the spectra of adjacency matrices multiplex networks under random matrix theory (RMT) framework. Through extensive numerical experiments, we demonstrate that upon multiplexing two networks, combined network exhibit superposition Gaussian orthogonal ensemble (GOE)s for very small strength followed by a smooth transition to GOE statistics with an increase in strength. Interestingly, randomness connection architecture, introduced rewiring 1D lattice, at least one layer may govern nearest neighbor spacing distribution (NNSD) entire network, and fact, can drive from Poisson or vice versa. Notably, this transpires number corresponding small-world transition. Ergo, only being represented is enough yield network. Spectra underlying interaction have been contemplated be related dynamical behaviour complex systems, investigations presented here implications achieving better structural control systems against perturbation layers.