The value of peripheral nodes in controlling multilayer networks

Abstract

We analyze the controllability of a two-layer network, where driver nodes can be chosen only from one layer. Each layer contains a scale-free network with directed links. The dynamics of nodes depends on the incoming links from other nodes (reputation dynamics). We find that the controllable part of the network is larger when choosing peripherial nodes to connect the two layers. The control is as efficient for peripherial nodes as driver nodes as it is for more central nodes. If we assume a cost to utilize nodes which is proportional to their degree, utilizing peripherial nodes to connect the two layers or to act as driver nodes is not only the most cost-efficient solution, it is also the one that gives us the best performance in controlling the two-layer network.