In an embodiment, a P2P device discovers other P2P devices that belong to a P2P group. The P2P device calculates a reachability vector that indicates each discovered P2P device within a threshold number of P2P hops. The P2P device receives reachability vector(s) for each proximate P2P device in a set of proximate P2P devices discovered via the P2P discovery procedure. The P2P device ranks the P2P device and each proximate P2P device in the set of proximate P2P devices based on the calculated and received reachability vectors. The P2P device identifies a leader (e.g., the P2P device itself and/or one or more of the other P2P devices) that is responsible for performing a floor arbitration function for a P2P session from the ranked P2P devices based on the rankings, and participates in the P2P session by exchanging media in accordance with the floor arbitration function performed by the leader.