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Numerous models have been proposed for modeling social networks to explore their structure or to address application problems, such as community detection and behavior prediction. However, the results are still far from satisfactory. One of the biggest challenges is how to capture all the information of a social network in a unified manner, such as links, communities, user attributes, roles and behaviors. In this paper, we propose a unified probabilistic framework, the Community Role Model (CRM), to model a social network. CRM incorporates all the information of nodes and edges that form a social network. We propose methods based on Gibbs sampling and an EM algorithm to estimate the model's parameters and fit our model to real social networks. Real data experiments show that CRM can be used not only to represent a social network, but also to handle various application problems with better performance than a baseline model, without any modification to the model, showing its great advantages.

Probabilistic Community and Role Model for Social Networks