  In this article we introduce a dynamic Erd\H{o}s-R\'enyi graph model, in
which, independently for each vertex pair, edges appear and disappear according
to a Markov on-off process. In studying the dynamic graph we present two main
results. The first being on how long it takes for the graph to reach
stationarity. We give an explicit expression for this time, as well as proving
that this is the fastest time to reach stationarity among all strong stationary
times. The second result concerns the time it takes for the dynamic graph to
reach a certain number of edges. We give an explicit expression for the
expected value of such a time, as well as study its asymptotic behavior. This
time is related to the first time the dynamic Erd\H{o}s-R\'enyi graph contains
a cluster exceeding a certain size.
