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Multilayer directed random networks: Scaling of spectral properties

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  • Tapia-Labra, G.
  • Hernández-Sánchez, M.
  • Méndez-Bermúdez, J.A.

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 β of the eigenfunctions of MDRNs follows a simple scaling law given by β=x∗/(1+x∗), where x∗ is a nontrivial function of M, N, and number of 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∗. We validate our results on real-world networks.

Suggested Citation

  • Tapia-Labra, G. & Hernández-Sánchez, M. & Méndez-Bermúdez, J.A., 2025. "Multilayer directed random networks: Scaling of spectral properties," Chaos, Solitons & Fractals, Elsevier, vol. 199(P2).
    • Handle: RePEc:eee:chsofr:v:199:y:2025:i:p2:s0960077925007088
    DOI: 10.1016/j.chaos.2025.116695
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    References listed on IDEAS

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    1. Hao Wu & Qiao Liang & Kaibo Wang, 2024. "Modeling and monitoring multilayer attributed weighted directed networks via a generative model," IISE Transactions, Taylor & Francis Journals, vol. 56(8), pages 902-914, August.
    2. Su, Wenqing & Guo, Xiao & Chang, Xiangyu & Yang, Ying, 2024. "Spectral co-clustering in multi-layer directed networks," Computational Statistics & Data Analysis, Elsevier, vol. 198(C).
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