We propose a Bayesian nonparametric prior for time-varying networks. To each node of the networ k is associated a positive parameter\, modeling t he sociability of that nodes. Sociabilities are as sumed to evolve over time\, and are modeled via a dynamic point process model. The model is able to (a) capture smooth evolution of the interactions between nodes\, allowing edges to appear/disappe ar over time (b) capture long term evolution of th e sociabilities of the nodes (c) and yields spars e graphs\, where the number of edges grows subqua dratically with the number of nodes. The evolution of the sociabilities is described by a tractable time-varying gamma process. We provide some theo retical insights into the model\, describe a Hamil tonian Monte Carlo algorithm for efficieent explo ration of the posterior distribution and present results on synthetic and real world dataset. LOCATION:Seminar Room 1\, Newton Institute CONTACT:INI IT END:VEVENT END:VCALENDAR