The study of complex networks has significantly advanced our understanding of community structures which serves as a crucial feature of real-world graphs. Detecting communities in graphs is a challenging problem with applications in sociology, biology, and computer science. Despite the efforts of an interdisciplinary community of scientists, a satisfactory solution to this problem has not yet been achieved. This review article delves into the topic of community detection in graphs, which serves as a crucial role in understanding the organization and functioning of complex systems. We begin by introducing the concept of community structure, which refers to the arrangement of vertices into clusters, with strong internal connections and weaker connections between clusters. Then, we provide a thorough exposition of various community detection methods, including a new method designed by us. Additionally, we explore real-world applications of community detection in diverse networks. In conclusion, this comprehensive review provides a deep understanding of community detection in graphs. It serves as a valuable resource for researchers and practitioners in multiple disciplines, offering insights into the challenges, methodologies, and applications of community detection in complex networks.

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