Quantifying concurrency in event-based temporal network and hypergraph data

Abstract: Many social, biological, and technological systems are recorded as sequences of time-stamped interactions. In such systems, concurrency, i.e., the tendency for an individual to participate in multiple interactions approximately at the same time, can strongly affect processes such as epidemic or information spreading. However, concurrency measures for event-based temporal network data are not established. We introduce edge-event correlation (EEC), a simple and interpretable measure that quantifies how similarly two connections are active over time. We apply EEC to empirical temporal networks and temporal hypergraphs, the latter allowing single events to involve more than two nodes. Across most datasets, pairs of edges or hyperedges that share a node show higher concurrency than pairs that do not. We further find that this elevated concurrency is mainly driven by pairs embedded in closed local structures, such as triangles in the aggregated network. EEC provides a practical tool for quantifying concurrency in event-based temporal data and may help identify network structures that facilitate rapid spreading or collective dynamics.