Entropy Rate of Diffusion Processes on Complex Networks

摘要

The concept of entropy rate for a dynamical process on a graph is introduced.We study diffusion processes where the node degrees are used as a localinformation by the random walkers. We describe analitically and numerically howthe degree heterogeneity and correlations affect the diffusion entropy rate. Inaddition, the entropy rate is used to characterize complex networks from thereal world. Our results point out how to design optimal diffusion processesthat maximize the entropy for a given network structure, providing a newtheoretical tool with applications to social, technological and communicationnetworks.