Overlapping communities and roles in networks with node attributes: Probabilistic graphical modeling, Bayesian formulation and variational inference

Community and role discovery are key tasks in network analysis. The former unveils the organization of a network, whereas the latter highlights the social functions of nodes. The integration of community discovery and role analysis has been investigated, to gain a deeper understanding of topology, i.e., the social functions fulfilled by nodes to pursue community purposes. However, hitherto, node attributes and behavioral role patterns have been ignored in the combination of both tasks. In this manuscript, we study the seamless integration of community discovery and behavioral role analysis, in the domain of networks with node attributes. In particular, we focus on unifying the two tasks, by explicitly harnessing node attributes and behavioral role patterns in a principled manner. To this end, we propose two Bayesian probabilistic generative models of networks, whose novelty consists in the interrelationship of overlapping communities, roles, their behavioral patterns and node attributes. The devised models allow for a variety of exploratory, descriptive and predictive tasks. These are carried out through mean-field variational inference, which is in turn mathematically derived and implemented into a coordinate-ascent algorithm.