Control of Multilayer Networks

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.

References in corpus (7)

• The structure and dynamics of multilayer networks
• Diffusion dynamics on multiplex networks
• Pinning-controllability of complex networks
• Control centrality and hierarchical structure in complex networks
• Avoiding catastrophic failure in correlated networks of networks
• Spectrum of Controlling and Observing Complex Networks
• Network Controllability Is Determined by the Density of Low In-Degree and Out-Degree Nodes

Cited by in corpus (13)

• Control Principles of Complex Networks
• The synchronized dynamics of time-varying networks
• Synchronization in networks with multiple interaction layers
• Controllability of multiplex, multi-timescale networks
• Value of peripheral nodes in controlling multilayer networks
• Network diffusion capacity unveiled by dynamical paths
• Interlayer antisynchronization in degree-biased duplex networks
• Diversity of structural controllability of complex networks with given degree sequence
• The evolution of network controllability in growing networks
• Higher-order models capture changes in controllability of temporal networks
• Statistical mechanics of bipartite $z$-matchings
• Multiscale modeling of brain network organization
• Structural Controllability of a Consensus Network with Multiple Leaders