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.

翻译：复杂网络的研究极大地促进了我们对社区结构的理解，而社区结构正是真实世界图数据的关键特征。图社区检测是一个具有挑战性的问题，在社会学、生物学和计算机科学中均有应用。尽管跨学科的科学界付出了诸多努力，但至今仍未找到令人满意的解决方案。本综述深入探讨了图社区检测这一主题，它在理解复杂系统的组织与运作中起着关键作用。我们首先介绍社区结构的概念，该概念指的是顶点聚集成簇的结构，其中簇内连接紧密而簇间连接稀疏。随后，我们详尽阐述了多种社区检测方法，包括我们自行设计的一种新方法。此外，我们还探讨了社区检测在多种网络中的实际应用。最后，本全面综述为图社区检测提供了深刻见解。它可作为多学科研究人员与实践者的宝贵资源，涵盖挑战、方法论及应用等方面，助力理解复杂网络中的社区检测。