Accelerating networks

Abstract

Evolving out-of-equilibrium networks have been under intense scrutiny recently. In many real-world settings the number of links added per new node is not constant but depends on the time at which the node is introduced in the system. This simple idea gives rise to the concept of accelerating networks, for which we review an existing definition and-after finding it somewhat constrictive-offer a new definition. The new definition provided here views network acceleration as a time dependent property of a given system as opposed to being a property of the specific algorithm applied to grow the network. The definition also covers both unweighted and weighted networks. As time-stamped network data becomes increasingly available, the proposed measures may be easily applied to such empirical datasets. As a simple case study we apply the concepts to study the evolution of three different instances of Wikipedia, namely, those in English, German, and Japanese, and find that the networks undergo different acceleration regimes in their evolution. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.