Entropy rate of diffusion processes on complex networks

We introduce the concept of entropy rate to characterize a diffusion process on a complex network. The entropy rate represents the minimal amount of information necessary to describe the diffusion on the network, and is a quantity extremely sensitive to the network topology and dynamics. By opportunely tuning the kind of diffusion, the entropy rate allows one to extract different properties of the network structure. Moreover, entropy maximization indicates how to design optimal diffusion processes, providing a new theoretical tool with applications to social, technological, and communication systems.