A new framework for dynamical models on multiplex networks

Many complex systems have natural representations as multilayer networks. While these formulations retain more information than standard single-layer network models, there is not yet a fully developed theory for computing network measures and statistics on these objects. We introduce a family of models of multiplex processes motivated by dynamical applications and investigate the properties of their spectra both theoretically and computationally. We study special cases of diffusion and Markov dynamics, using the spectral results to compute their rates of convergence. We use our framework to define a version of multiplex eigenvector centrality, which generalizes some existing notions in the literature. Last, we compare our operator to structurally derived models on synthetic and real-world networks, helping delineate the contexts in which the different frameworks are appropriate.