Random walk centrality in interconnected multilayer networks

•We provide analytical expressions for the centrality of random walks in interconnected multilayer networks.•We check the theoretical results with extensive Monte Carlo simulations of random walkers in different topologies, and achieve an excellent agreement.•Our results are useful for the ranking of nodes in multi-categorical systems.

Real-world complex systems exhibit multiple levels of relationships. In many cases they require to be modeled as interconnected multilayer networks, characterizing interactions of several types simultaneously. It is of crucial importance in many fields, from economics to biology and from urban planning to social sciences, to identify the most (or the less) influent nodes in a network using centrality measures. However, defining the centrality of actors in interconnected complex networks is not trivial. In this paper, we rely on the tensorial formalism recently proposed to characterize and investigate this kind of complex topologies, and extend two well known random walk centrality measures, the random walk betweenness and closeness centrality, to interconnected multilayer networks. For each of the measures we provide analytical expressions that completely agree with numerically results.