Dynamical Processes in Time-Varying Networks

Abstract

Networks in almost any domain are dynamical entities. New nodes join the system, others leave it, and links describing their interactions are constantly changing. However, due to the absence of time-resolved data and mathematical challenges, the large majority of research in network science neglects these features in favor of static or mean-field representations. While such approximations are useful and appropriate in some systems and processes, they fail in many others where the co-occurrence, duration, and order of contacts are crucial ingredients. This chapter presents a review of recent developments in the study of temporal networks and dynamical processes unfolding on their fabrics. It focuses in particular on activity-driven networks as an empirically motivated and analytically tractable class of models of the time-varying network. Within this framework the chapter studies the effects of temporal connectivity patterns in random walks, the epidemic model, and the rumor spreading model. The results highlight the striking impact that temporal correlations have on dynamical processes taking place over time-varying networks. The chapter ends by considering future research directions and challenges in this important area.