# Spacing ratio statistics of multiplex directed networks

## TL;DR

This paper investigates eigenvalue ratio statistics of multiplex directed networks using random matrix theory, revealing how multiplexing strength influences spectral properties and eigenvector delocalization.

## Contribution

It introduces a numerical analysis of eigenvalue ratio statistics in multiplex directed networks represented by non-Hermitian and Hermitian matrices, highlighting the role of multiplexing strength.

## Key findings

- Multiplexing strength governs eigenvalue ratio statistics.
- Multiplexing strength influences eigenvector delocalization.
- Results applicable to understanding dynamics in multilayer systems.

## 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 Erdos-Renyi 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 behavior 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 the significance of multiplexing in comprehending network properties.