This study aims to infer the social nature of conversations from their content automatically. To place this work in context, our motivation stems from the need to understand how social disengagement affects cognitive decline or depression among older adults. For this purpose, we collected a comprehensive and naturalistic corpus comprising of all the incoming and outgoing telephone calls from 10 subjects over the duration of a year. As a first step, we learned a binary classifier to filter out business related conversation, achieving an accuracy of about 85%. This classification task provides a convenient tool to probe the nature of telephone conversations. We evaluated the utility of openings and closing in differentiating personal calls, and find that empirical results on a large corpus do not support the hypotheses by Schegloff and Sacks that personal conversations are marked by unique closing structures. For classifying different types of social relationships such as family vs other, we investigated features related to language use (entropy), hand-crafted dictionary (LIWC) and topics learned using unsupervised latent Dirichlet models (LDA). Our results show that the posteriors over topics from LDA provide consistently higher accuracy (60-81%) compared to LIWC or language use features in distinguishing different types of conversations.