Unlike a simple network with just nodes and edges in between them, the real-world networks can contain much more, such as a set of attributes associated with every node in the network. These networks opened up a new avenue in community detection called attributed graph clustering (AGC). Furthermore, the clusters in real-world are not usually disjoint, as compared to most of the work that has been carried out in the field of AGC. This raises a need for AGC with fuzzy clusters. In this work, we try to comprehend the problem of attributed graph clustering with the help of a game-theoretic approach called dynamic cluster formation game (DCFG). To address the possibility of fuzzy clusters in a network, we model the problem of AGC as a series of coupled games involving mixed strategies, in contrast to the previous work that was primarily focused on pure strategy equilibrium. We discuss the convergence of the proposed game and the existence of Nash equilibrium at convergence. We also propose a clustering algorithm which uses a game-theoretic approach to partition a network into fuzzy clusters, giving a solution balanced in terms of topology and node attributes. We compare the the results of our work to the state-of-the-art clustering methods available in the literature.

与仅具有节点和边缘之间的简单网络不同，真实世界的网络可以包含更多内容，例如与网络中每个节点关联的一组属性。这些网络为社区检测开辟了一条新途径，称为属性图聚类（AGC）。此外，与AGC领域中已开展的大多数工作相比，现实世界中的集群通常并不脱节。这就需要具有模糊聚类的AGC。在这项工作中，我们尝试借助一种称为动态聚类形成游戏（DCFG）的博弈论方法来理解属性图聚类的问题。为了解决网络中模糊聚类的可能性，我们将AGC问题建模为一系列涉及混合策略的耦合博弈，与之前的工作主要集中在纯策略均衡上形成对比。我们讨论了拟议博弈的收敛性和收敛时纳什均衡的存在。我们还提出了一种聚类算法，该算法使用博弈论方法将网络划分为模糊聚类，从而提供一种在拓扑和节点属性方面保持平衡的解决方案。我们将工作结果与文献中提供的最新聚类方法进行比较。