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With the growing explosion of online social networks, the study of large-scale graph clustering has attracted considerable interest. Most of traditional methods view the graph clustering problem as an optimization problem based on a given objective function; however, there are few methodical theories for the emergence of clusters over real-life networks. In this paper, each actor in online social networks is viewed as a selfish player in a non-cooperative game. The strategy associated with each node is defined as the cluster membership vector, and each one’s incentive is to maximize its own social identity by adopting the most suitable strategy. The definition of utility function in our game model is inspired by the conformity psychology, which is defined as the weighted average of one’s social identity by participating different clusters. With this setting, the proposed game can well match a potential game. So that …