Community discovery and role assignment have been recently integrated into an unsupervised approach for the exploratory analysis of overlapping communities and inner roles in networks. However, the formation of ties in these prototypical research efforts is not truly realistic, since it does not account for a fundamental aspect of link establishment in real-world networks, i.e., the explicative reasons that cause interactions among nodes. Such reasons can be interpreted as generic requirements of nodes, that are met by other nodes and essentially pertain both to the nodes themselves and to their interaction contexts (i.e., the respective communities and roles). In this article, we present two new model-based machine-learning approaches, wherein community discovery and role assignment are seamlessly integrated and simultaneously performed through approximate posterior inference in Bayesian mixed-membership models of directed networks. The devised models account for the explicative reasons governing link establishment in terms of node-specific and contextual latent interaction factors. The former are inherently characteristic of nodes, while the latter are characterizations of nodes in the context of the individual communities and roles.The generative process of both models assigns nodes to communities with respective roles and connects them through directed links, which are probabilistically governed by their node-specific and contextual interaction factors. The difference between the proposed models lies in the exploitation of the contextual interaction factors. More precisely, in one model, the contextual interaction factors have the same impact on link generation. In the other model, the contextual interaction factors are weighted by the extent of involvement of the linked nodes in the respective communities and roles. We develop MCMC algorithms implementing approximate posterior inference and parameter estimation within our models. Finally, we conduct an intensive comparative experimentation, which demonstrates their superiority in community compactness and link prediction on various real-world and synthetic networks.
