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增进了我们对社区结构的理解，而社区结构正是真实世界图的一个关键特征。检测图中的社区是一项具有挑战性的问题，在社会学、生物学和计算机科学中均有应用。尽管跨学科科学家群体付出了努力，但尚未能找到令人满意的解决方案。本综述文章深入探讨了图中的社区检测这一主题，它在理解复杂系统的组织与运行中起着至关重要的作用。我们首先介绍社区结构的概念，即顶点聚集成簇，且簇内连接紧密、簇间连接稀疏的排列方式。随后，我们全面阐述了各类社区检测方法，包括我们自己设计的一种新方法。此外，我们还探讨了社区检测在不同网络中的实际应用。总之，这篇全面的综述使读者对图中的社区检测有了深入理解。作为多学科领域研究人员与实践者的宝贵资源，它提供了对复杂网络中社区检测的挑战、方法及应用的深刻洞见。