1. Multilayer directed random networks: Scaling of spectral properties
- Author
-
Tapia-Labra, G., Hernández-Sánchez, M., and Méndez-Bermúdez, J. A.
- Subjects
Condensed Matter - Disordered Systems and Neural Networks ,Physics - Data Analysis, Statistics and Probability - Abstract
Motivated by the wide presence of multilayer networks in both natural and human-made systems, within a random matrix theory (RMT) approach, in this study we compute eigenfunction and spectral properties of multilayer directed random networks (MDRNs) in two setups composed by $M$ layers of size $N$: A line and a complete graph (node-aligned multiplex network). First, we numerically demonstrate that the normalized localization length $\beta$ of the eigenfunctions of MDRNs follows a simple scaling law given by $\beta=x^*/(1+x^*)$, with $x^*\propto (b_{\rm eff}^2/L)^\delta$, $\delta\sim 1$ and $b_{\rm eff}$ being the effective bandwidth of the adjacency matrix of the network of size $L=M\times N$. Here, $b_{\rm eff}$ incorporates both intra- and inter-layer edges. Then, we show that other eigenfunction and spectral RMT measures (the inverse participation ratio of eigenfunctions, the ratio between nearest- and next-to-nearest-neighbor eigenvalue distances, and the ratio between consecutive singular-value spacings) of MDRNs also scale with $x^*$., Comment: 11 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:2406.15426, arXiv:1611.06695
- Published
- 2024