The massive scale of online social networks makes it very challenging to characterize the underlying structure therein. In this paper, we employ the t-cherry junction tree, a very recent advancement in probabilistic graphical models, to develop a compact representation and good approximation of an otherwise intractable model for users' relationships in a social network. There are a number of advantages in this approach: 1) the best approximation possible via junction trees belongs to the class of t-cherry junction trees; 2) constructing a t-cherry junction tree can be largely parallelized; and 3) inference can be performed using distributed computation. To improve the quality of approximation, we also devise an algorithm to build a higher order tree gracefully from an existing one, without constructing it from scratch. We apply this approach to Twitter data containing 100,000 nodes and study the problem of recommending connections to new users.