Convergence of Dynamics on Networks

We view information flow as a dynamical process on networks, and discuss the convergence (or lack thereof) to equilibrium states. Based on graph theory and dynamical systems concepts, we present a common framework that allows the analysis of several problems, such as random walks, ergodicity, synchronization, opinion spread, etc. Furthermore, this approach reveals some unifying principles that underlie seemingly different processes. Finally, we discuss the role of information transmission delays in dynamics.