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.

翻译：本文考虑一种动态Erdős-Rényi图，其中边根据交替更新过程在存在与缺失状态之间切换。目标是在仅观测到边的总数量的情况下，估计通断时间分布。这一逆问题在参数化框架下通过基于矩估计法构建的估计量来解决。我们给出了估计量渐近正态性的条件，并指出了如何识别相应的协方差矩阵。同时展示了若观测到替代子图计数（如楔形或三角形数量），如何调整估计过程。