  While a natural fit for modeling and understanding mobile networks,
time-varying graphs remain poorly understood. Indeed, many of the usual
concepts of static graphs have no obvious counterpart in time-varying ones. In
this paper, we introduce the notion of temporal reachability graphs. A
(tau,delta)-reachability graph} is a time-varying directed graph derived from
an existing connectivity graph. An edge exists from one node to another in the
reachability graph at time t if there exists a journey (i.e., a spatiotemporal
path) in the connectivity graph from the first node to the second, leaving
after t, with a positive edge traversal time tau, and arriving within a maximum
delay delta. We make three contributions. First, we develop the theoretical
framework around temporal reachability graphs. Second, we harness our
theoretical findings to propose an algorithm for their efficient computation.
Finally, we demonstrate the analytic power of the temporal reachability graph
concept by applying it to synthetic and real-life datasets. On top of defining
clear upper bounds on communication capabilities, reachability graphs highlight
asymmetric communication opportunities and offloading potential.
