Peer-to-peer systems are known to be vulnerable to the Sybil attack. The lack of a central authority allows a malicious user to create many fake identities (called Sybil nodes) pretending to be independent honest nodes. The goal of the malicious user is to influence the system on his/her behalf. In order to detect the Sybil nodes and prevent the attack, a reputation system is used for the nodes, built through observing its interactions with its peers. The construction makes every node a part of a distributed authority that keeps records on the reputation and behavior of the nodes. Records of interactions between nodes are broadcast by the interacting nodes and honest reporting proves to be a Nash Equilibrium for correct (non-Sybil) nodes. In this research is argued that in realistic communication schedule scenarios, simple graph-theoretic queries such as the computation of Strongly Connected Components and Densest Subgraphs, help in exposing those nodes most likely to be Sybil, which are then proved to be Sybil or not through a direct test executed by some peers.