This article proposes methods to model non-stationary temporal graph processes motivated by a hospital interaction data set. This corresponds to modelling the observation of edge variables indicating interactions between pairs of nodes exhibiting dependence and evolution in time over interactions. This article thus blends (integer) time series models with flexible static network models to produce models of temporal graph data, and statistical fitting procedures for time-varying interaction data. We illustrate the power of our proposed fitting method by analysing a hospital contact network, and this shows the challenge in modelling and inferring correlation between a large number of variables.