  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.
