Graph clustering algorithms are essential tools for partitioning complex networks into meaningful clusters, which helps reveal hidden relationships and maximize intra-cluster edge density while minimizing inter-cluster connections. These algorithms are crucial for various applications across domains such as social network analysis, bioinformatics, recommendation systems, and transportation network optimization. Different types of graph clustering methods, including hierarchical clustering, modularity-based algorithms, label propagation, spectral clustering, and edge betweenness, each offer unique strengths tailored to specific graph structures and analysis goals. The choice of an appropriate algorithm depends on factors like graph size, structure, analysis goals, computational efficiency, scalability, and interpretability. As the complexity and scale of graph data continue to grow, innovations like Graph Neural Networks (GNNs) are expected to address advanced clustering challenges, driving deeper insights and impactful solutions across industries.