The temporal event graph

Temporal networks are increasingly being used to model the interactions of complex systems. Most studies require the temporal aggregation of edges (or events) into discrete time steps to perform analysis. In this article, we describe a static, behavioural representation of a temporal network, the temporal event graph (TEG). The TEG describes the temporal network in terms of both inter-event time and two-event temporal motifs. By considering the distributions of these quantities in unison, we provide a new method to characterize the behaviour of individuals and collectives in temporal networks as well as providing a natural decomposition of the network. We illustrate the utility of the TEG by providing examples on both synthetic and real temporal networks.