Although users of online communication tools rarely categorize their contacts into groups such as "family", "co-workers", or "jogging buddies", they nonetheless implicitly cluster contacts, by virtue of their interactions with them, forming implicit groups. In this paper, we describe the implicit social graph which is formed by users' interactions with contacts and groups of contacts, and which is distinct from explicit social graphs in which users explicitly add other individuals as their "friends". We introduce an interaction-based metric for estimating a user's affinity to his contacts and groups. We then describe a novel friend suggestion algorithm that uses a user's implicit social graph to generate a friend group, given a small seed set of contacts which the user has already labeled as friends. We show experimental results that demonstrate the importance of both implicit group relationships and interaction-based affinity ranking in suggesting friends. Finally, we discuss two applications of the Friend Suggest algorithm that have been released as Gmail Labs features.