We introduce a new Bayesian admixture model intended for exploratory analysis of communication networks-specifically, the discovery and visualization of topic-specific subnetworks in email data sets. Our model produces principled visualizations of email networks, i.e., visualizations that have precise mathematical interpretations in terms of our model and its relationship to the observed data. We validate our modeling assumptions by demonstrating that our model achieves better link prediction performance than three state-of-the-art network models and exhibits topic coherence comparable to that of latent Dirichlet allocation. We showcase our model's ability to discover and visualize topic-specific communication patterns using a new email data set: the New Hanover County email network. We provide an extensive analysis of these communication patterns, leading us to recommend our model for any exploratory analysis of email networks or other similarly-structured communication data. Finally, we advocate for principled visualization as a primary objective in the development of new network models.