This paper reviews the advancements in federated graph clustering, a technique that combines graph theory with federated learning to enable clustering analysis on distributed data while ensuring privacy. By allowing multiple data holders to collaboratively construct and optimize clustering models without sharing raw data, federated graph clustering proves especially relevant in sensitive domains such as healthcare, finance, and social networks, where data is often decentralized. We analyze existing algorithms, evaluating their performance and benefits across various applications, and address challenges including communication efficiency, model convergence, and scalability. This review underscores the considerable potential of federated graph clustering for cross-domain collaboration and privacy preservation, advocating for further research to enhance the practicality and scalability of algorithms to meet the growing demand for data analysis in privacy-sensitive environments.