  In this paper we consider a dynamic Erd\H{o}s-R\'enyi graph in which edges,
according to an alternating renewal process, change from present to absent and
vice versa. The objective is to estimate the on- and off-time distributions
while only observing the aggregate number of edges. This inverse problem is
dealt with, in a parametric context, by setting up an estimator based on the
method of moments. We provide conditions under which the estimator is
asymptotically normal, and we point out how the corresponding covariance matrix
can be identified. It is also demonstrated how to adapt the estimation
procedure if alternative subgraph counts are observed, such as the number of
wedges or triangles.
