Perron communicability and sensitivity of multilayer networks

Modeling complex systems that consist of different types of objects leads to mul- tilayer networks, where nodes in the different layers represent different kinds of objects. Nodes are connected by edges, which have positive weights. A multilayer network is associated with a supra-adjacency matrix. This paper investigates the sensitivity of the communicability in a multilayer network to perturbations of the network by studying the sensitivity of the Perron root of the supra-adjacency matrix. Our analysis sheds light on which edge weights to make larger to increase the com- municability of the network, and which edge weights can be made smaller or set to zero without affecting the communicability significantly.