  We create a framework to analyse the timing and frequency of instantaneous
interactions between pairs of entities. This type of interaction data is
especially common nowadays, and easily available. Examples of instantaneous
interactions include email networks, phone call networks and some common types
of technological and transportation networks. Our framework relies on a novel
extension of the latent position network model: we assume that the entities are
embedded in a latent Euclidean space, and that they move along individual
trajectories which are continuous over time. These trajectories are used to
characterize the timing and frequency of the pairwise interactions. We discuss
an inferential framework where we estimate the individual trajectories from the
observed interaction data, and propose applications on artificial and real
data.
