In the context of adaptive intelligent systems, it is essential to build user models to be considered with adaptation purposes. Personality is an interesting user feature to be incorporated in user models; it may lead to know the user needs or preferences in different situations. In this direction, eliciting user personality is needed. This information should be obtained as unobtrusively as possible, yet without compromising the reliability of the model built. In this paper, we present a method for eliciting user personality by analyzing user interactions within the social network Facebook, with the goal of mining behavioral patterns. We have developed TP2010, a Facebook application based on the ZKPQ-50-cc questionnaire, to get information about both the user personality and his interactions within Facebook. We have built a classifier model starting from the analysis of a set of data from more than 11000 users. The results show that it is feasible to get information about the user personality by analyzing data from social network interactions.