  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, lossless, and unique representation of a temporal network,
the temporal event graph (TEG). The TEG describes the temporal network in terms
of both the inter-event time and two-event temporal motif distributions. By
considering these distributions in unison we provide a new method to
characterise 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.
