Weighted Temporal Event Graphs and Temporal-Network Connectivity

Correlations between the times of events in a temporal network carry information on the function of the network and constrain how dynamical processes taking place on the network can unfold. Various techniques for extracting information from correlated event times have been developed, from the analysis of time-respecting paths to temporal motif statistics. In this chapter, we discuss a recently-introduced, general framework that maps the connectivity structure contained in a temporal network’s event sequence onto static, weighted graphs. This mapping retains all information on time-respecting paths and the time differences between their events. The weighted temporal event graph framework builds on directed, acyclic graphs (DAGs) that contain a superposition of all temporal paths of the network. We introduce the reader to the mapping from temporal networks onto DAGs and the associated computational methods and illustrate the power of this framework by applying it to temporal motifs and to temporal-network percolation.