Networks play a central role in modern data analysis, enabling us to reason about systems by studying the relationships between their parts. Most often in network analysis, the edges are given. However, in many systems it is difficult or impossible to measure the network directly. Examples of latent networks include economic interactions linking financial instruments and patterns of reciprocity in gang violence. In these cases, we are limited to noisy observations of events associated with each node. To enable analysis of these implicit networks, we develop a probabilistic model that combines mutually- exciting point processes with random graph models. We show how the Poisson superposition principle enables an elegant auxiliary variable formulation and a fully-Bayesian, parallel inference algorithm. We evaluate this new model empirically on several datasets.