Connectivity patterns between nodes in a computer network can be interpreted and modelled as point processes where events in a process indicate connections being established for data to be sent along that edge. A model of normal connectivity behaviour can be constructed for each edge in a network by identifying key network user features such as seasonality or self-exciting behaviour, since events typically arise in bursts at particular times of day which may be peculiar to that edge. When monitoring a computer network in real time, unusual patterns of activity against the model of normality could indicate the presence of a malicious actor. A flexible, novel, nonparametric model for the excitation function of a Wold process is proposed for modelling the conditional intensities of network edges. This approach is shown to outperform standard seasonality and self-excitation models in predicting network connections, achieving well-calibrated predictions for event data collected from the computer networks of both Imperial College and Los Alamos National Laboratory.