Spectral fluctuations and crossovers in multilayer network

TL;DR

This paper explores spectral fluctuations in multilayer networks using random matrix theory, revealing universal behaviors and a crossover from independent to unified spectral statistics as inter-layer connections vary.

Contribution

It introduces a crossover model for bilayer networks that captures spectral transitions from block-diagonal to single GOE statistics, extending RMT analysis to multilayer structures.

Findings

Spectral fluctuations exhibit universality across multilayer networks.

A crossover model describes spectral transition from independent to connected layers.

RMT effectively probes topological and dynamical features of real-world networks.

Abstract

We investigate spectral fluctuations in multilayer networks within the random matrix theory (RMT) framework to characterize universal and non-universal features. The adjacency matrix of a multilayer network exhibits a block structure, with diagonal blocks representing intra-layer connections and off-diagonal blocks encoding inter-layer connections. Applying appropriate scaling factors for these blocks, we equalize variances across inter- and intra-layers, enabling direct comparison of spectral statistics. We analyze eigenvalue spectra across multilayer network configurations with varying inter- and intra-layer connectivities. Introducing a crossover model for bilayer networks, we capture the smooth transition of spectral properties from block-diagonal (two independent GOEs) to single-layer (one GOE) statistics as the relative strength of inter-layer to intra-layer connection varies. Furthermore, we analyze interatomic distance networks derived from protein crystal structures, including 1EWT, 1EWK, and 1UW6, to demonstrate applicability. Our findings reveal that the universality of spectral fluctuations persists across multilayer network architectures and highlight RMT as a robust tool for probing topological and dynamical complexities of real-world networks.