  Modeling complex systems that consist of different types of objects leads to
multilayer networks, where nodes in the different layers represent different
kind 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 communicability of the network, and which edge
weights can be made smaller or set to zero without affecting the
communicability significantly.
