Remaining popular: power-law regularities in network dynamics

Abstract

The structure of networks has been a focal research topic over the past few decades. These research efforts have enabled the discovery of numerous structural patterns and regularities, bringing forth advancements in many fields. In particular, the ubiquitous power-law patterns evident in degree distributions, graph eigenvalues and human mobility patterns have provided the opportunity to model many different complex systems. However, regularities in the dynamical patterns of networks remain a considerably less explored terrain. In this study we examine the dynamics of networks, focusing on stability characteristics of node popularity, and present our results using various empirical datasets. Specifically, we address several intriguing questions – for how long are popular nodes expected to remain so? How much time is expected to pass between two consecutive popularity periods? What characterizes nodes which manage to maintain their popularity for long periods of time? Surprisingly, we find that such temporal aspects are governed by a power-law regime, and that these power-law regularities are equally likely across all node ages.