Multiple structural transitions in interacting networks

TL;DR

This paper investigates how interconnected multilayer networks undergo multiple structural transitions in their algebraic connectivity as inter-network interactions change, revealing new regimes and dependencies relevant for system robustness.

Contribution

It introduces a perturbative approach to analyze multiple structural transitions in interconnected networks and shows the dependence of algebraic connectivity growth on degree configuration, not topology.

Findings

Multiple structural transitions in algebraic connectivity identified.

Growth of algebraic connectivity depends on degree configuration, not interaction topology.

Perturbation theory applied to adjacency matrix helps characterize percolation processes.

Abstract

Many real-world systems can be modeled as interconnected multilayer networks, namely a set of networks interacting with each other. Here we present a perturbative approach to study the properties of a general class of interconnected networks as inter-network interactions are established. We reveal multiple structural transitions for the algebraic connectivity of such systems, between regimes in which each network layer keeps its independent identity or drives diffusive processes over the whole system, thus generalizing previous results reporting a single transition point. Furthermore we show that, at first order in perturbation theory, the growth of the algebraic connectivity of each layer depends only on the degree configuration of the interaction network (projected on the respective Fiedler vector), and not on the actual interaction topology. Our findings can have important implications in the design of robust interconnected networked system, particularly in the presence of network layers whose integrity is more crucial for the functioning of the entire system. We finally show results of perturbation theory applied to the adjacency matrix of the interconnected network, which can be useful to characterize percolation processes on such systems.