Interdependent effects of cohesion and concurrency for epidemic potential

Purpose: Network diffusion depends on both the pattern and timing of relations, but the relative effects of timing and structure remain unclear. Here, we first show that concurrency (relations that overlap in time) increases epidemic potential by opening new routes in the network. Because this is substantively similar to adding contact paths, we next compare the effects of concurrency by observed levels of path redundancy (structural cohesion) to determine how the features interact. Methods: We establish that concurrency increases exposure analytically and then use simulation methods to manipulate concurrency over observed networks that vary naturally on structural cohesion. This design allows us to compare networks across a wide concurrency range holding constant features that might otherwise conflate concurrency and cohesion. We summarize the simulation results with general linear models. Results: Our results indicate interdependent effects of concurrency and structural cohesion: although both increase epidemic potential, concurrency matters most when the graph structure is sparse, because the exposure created by concurrency is redundant to observed paths within structurally cohesive networks. Conclusions: Concurrency works by opening new paths in temporally ordered networks. Because this is substantively similar to having additional observed paths, concurrency in sparse networks has the same effect as adding relations and will have the greatest effect on epidemic potential in sparse networks.