Discrete-time distributed consensus on multiplex networks

Abstract

We introduce a discrete-time distributed consensus process on multi-layered complex networks represented by multiplex graphs. The proposed consensus process can be characterized with a multiplex Markov chain (MC) composed of a mixture of interlayer and intralayer MCs. The interlayer MC is characterized by a parameter which represents the probability that the chain will switch between different layers of the multiplex network. Surprisingly, for large regions of the parameter space the convergence speed of the multiplex MC is determined only by the convergence speed of the interlayer MC. Moreover, as the number of layers in the network is increased, these regions increase until they encompass the whole parameter space. We also show that for some regions of the parameter space, the multiplex MC has a faster convergence speed than the MCs on top of the individual layers, thus complementing previous results on diffusion on multiplex networks.