In this paper, we present a case study describing the privacy and trust that exist within a small population of online social network users. We begin by formally characterizing different graphs in social network sites like Facebook. We then determine how often people are willing to divulge personal details to an unknown online user, an adversary. While most users in our sample did not share sensitive information when asked by an adversary, we found that more users were willing to divulge personal details to an adversary if there is a mutual friend connected to the adversary and the user. We then summarize the results and observations associated with this Facebook case study.