Exploring concurrency and reachability in the presence of high temporal resolution

Network properties govern the rate and extent of spreading processes on networks, from simple contagions to complex cascades. Recent advances have extended the study of spreading processes from static networks to temporal networks, where nodes and links appear and disappear. We review previous studies on the effects of temporal connectivity for understanding the spreading rate and outbreak size of model infection processes. We focus on the effects of "accessibility", whether there is a temporally consistent path from one node to another, and "reachability", the density of the corresponding "accessibility graph" representation of the temporal network. We study reachability in terms of the overall level of temporal concurrency between edges, quantifying the overlap of edges in time. We explore the role of temporal resolution of contacts by calculating reachability with the full temporal information as well as with a simplified interval representation approximation that demands less computation. We demonstrate the extent to which the computed reachability changes due to this simplified interval representation.