Social networks play an increasingly important role in today's society. Special characteristics of these networks make them challenging domains for the search community. In particular, social networks of users can be viewed as search graphs of nodes, where the cost of obtaining information about a node can be very high. This paper addresses the search problem of identifying the degree of separation between two users. New search techniques are introduced to provide optimal or near-optimal solutions. The experiments are performed using Twitter, and they show an improvement of several orders of magnitude over greedy approaches. Our optimal algorithm finds an average degree of separation of 3.43 between two random Twitter users, requiring an average of only 67 requests for information over the Internet to Twitter. A near-optimal solution of length 3.88 can be found by making an average of 13.3 requests.