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Besides the topological structure, there are additional information, i.e., node attributes, on top of the plain graphs. Usually, these systems can be well modeled by attributed graphs, where nodes represent component actors, a set of attributes describe users' portraits and edges indicate their connections. An elusive question associated with attributed graphs is to study how clusters with common internal properties form and evolve in real-world networked systems with great individual diversity, which leads to the so-called problem of attributed graph clustering (AGC). In this paper, we comprehended AGC naturally as a dynamic cluster formation game (DCFG), where each node's feasible action set can be constrained by every cluster in a discrete-time dynamical system. Specifically, we carried out a deep research on a special case of finite dynamic games, named dynamic social game (DSG), the convergence of the …