A stochastic block model for interaction lengths

We propose a new stochastic block model that focuses on the analysis of interaction lengths in dynamic networks. The model does not rely on a discretization of the time dimension and may be used to analyze networks that evolve continuously over time. The framework relies on a clustering structure on the nodes, whereby two nodes belonging to the same latent group tend to create interactions and non-interactions of similar lengths. We introduce a variational expectation–maximization algorithm to perform inference, and adapt a widely used clustering criterion to perform model choice. Finally, we validate our methodology using simulated data experiments and showing two illustrative applications concerning face-to-face interaction data and a bike sharing network.