Random matrix analysis of Multilayer Networks*

We investigate the spectra of adjacency matrices of multilayer networks under random matrix theory (RMT) framework. Through numerical experiments, we show that the randomness in the connection architecture of at least one layer may govern NNSD of the entire multilayer network, and in fact, can lead to a transition from the Poisson to GOE statistics or vice versa by changing random connections in only one of its layers. Additionally, one of the layers being substituted by a random network dominates the spectral fluctuations of the entire multiplex networks irrespective of network architecture or multiplexing strength of another layer. To conclude, these numerical experiments suggest that small multiplexing supports regularity in the spectra captured through NNSD whereas an increase in multiplexing leads to randomness. These investigations have implications in providing the structural and dynamical control of entire systems represented by multilayer networks due to structural perturbation in only one of the layers.