This research concerns the analysis of social networks using graph theory to find properties that can be used to determine Sybil nodes. This research also investigated the mixing time, which is one of the properties that many existing methods use for detecting Sybil attacks. The results showed that the mixing time does not reflect the difference between honest graphs and Sybil graphs. In addition, the properties of social graphs were studied and it was found that the average node distance is different in graphs containing Sybil nodes than in graphs with only honest nodes. Furthermore, the eigenvector centrality and the degree of Sybil nodes are correlated, while in honest nodes they are not.