Spacing ratio statistics of multiplex directed networks

Abstract

Eigenvalues statistics of various many-body systems have been widely
studied using the nearest neighbor spacing distribution under the random matrix
theory framework. Here, we numerically analyze eigenvalue ratio statistics of multiplex
networks consisting of directed Erd ̋os-R ́enyi random networks layers represented as,
first, weighted non-Hermitian random matrices and then weighted Hermitian random
matrices. We report that the multiplexing strength rules the behaviour of average
spacing ratio statistics for multiplexing networks represented by the non-Hermitian
and Hermitian matrices, respectively. Additionally, for both these representations
of the directed multiplex networks, the multiplexing strength appears as a guiding
parameter for the eigenvector delocalization of the entire system. These results could be important for driving dynamical processes in
several real-world multilayer systems, particularly, understanding significance of the
multiplexing in comprehending network properties.

Smallworldness in hypergraphs

“…The small-world phenomenon-the principle that we are all linked by short chains of acquaintances-is all about the abundance of short paths in a network. There exists an interplay between the structural and dynamical features of networked systems, former crucially affecting the later behavior [29,30]. For example, analysis of network structural properties helps in understanding robustness, efficiency of information transmission, and resiliency [31].…”