Control of Multilayer Networks

TL;DR

This paper develops a theoretical framework for understanding the controllability of multilayer networks, revealing how inter-layer correlations affect robustness and stability.

Contribution

It introduces a novel approach to analyze multilayer network controllability by mapping it to a combinatorial matching problem, extending prior isolated network studies.

Findings

Correlating external signals reduces network robustness to node removal.

Hybrid phase transition observed in interacting Poisson networks.

Multilayer networks can stabilize controllability even when single networks are unstable.

Abstract

The controllability of a network is a theoretical problem of relevance in a variety of contexts ranging from financial markets to the brain. Until now, network controllability has been characterized only on isolated networks, while the vast majority of complex systems are formed by multilayer networks. Here we build a theoretical framework for the linear controllability of multilayer networks by mapping the problem into a combinatorial matching problem. We found that correlating the external signals in the different layers can significantly reduce the multiplex network robustness to node removal, as it can be seen in conjunction with a hybrid phase transition occurring in interacting Poisson networks. Moreover we observe that multilayer networks can stabilize the fully controllable multiplex network configuration that can be stable also when the full controllability of the single network is not stable.