A new class of models for dynamic networks is proposed, called mutually exciting point process graphs (MEG). MEG is a scalable network-wide statistical model for point processes with dyadic marks, which can be used for anomaly detection when assessing the significance of future events, including previously unobserved connections between nodes. The model combines mutually exciting point processes to estimate dependencies between events and latent space models to infer relationships between the nodes. The intensity functions for each network edge are characterized exclusively by node-specific parameters, which allows information to be shared across the network. This construction enables estimation of intensities even for unobserved edges, which is particularly important in real world applications, such as computer networks arising in cyber-security. A recursive form of the log-likelihood function for MEG is obtained, which is used to derive fast inferential procedures via modern gradient ascent algorithms. An alternative EM algorithm is also derived. The model and algorithms are tested on simulated graphs and real world datasets, demonstrating excellent performance. Supplementary materials for this article are available online.