Online social networks have become major and driving phenomena on the Web. In this talk we focus on some structural and algorithmic questions related to large online social networks. We formulate a simple and general model of social networks that can explain the success of Milgram's famous experiment that gave rise to `six-degrees of separation'. We then study the neighborhood connectivity structure of users in a social network, where two users are connected if they share a common interest; we propose an efficient algorithm in this context.