The chapter "Community Detection in Graphs" by Santo Fortunato provides a comprehensive overview of the field of community detection in graphs, which is crucial for understanding complex systems. The main focus is on the organization of vertices into clusters, known as communities, where edges within clusters are more common than between clusters. These communities are analogous to tissues or organs in biological systems and play significant roles in various disciplines such as sociology, biology, and computer science. The chapter begins by introducing the concept of community structure in real-world networks, highlighting examples from social networks, protein-protein interaction networks, and technological networks. It emphasizes the importance of community detection in applications such as improving web services, customer segmentation, and efficient routing in ad hoc networks. The text then delves into the elements of community detection, including computational complexity, definitions of communities and partitions, and traditional methods like graph partitioning, hierarchical clustering, partitional clustering, and spectral clustering. It also discusses modern techniques such as divisive algorithms, modularity-based methods, spectral algorithms, dynamic algorithms, and methods based on statistical inference. The chapter explores the challenges and limitations of existing methods, particularly the issue of overlapping communities and the need for efficient algorithms to handle large networks. It provides a detailed discussion on the significance of clustering and the testing and comparison of algorithms. Finally, the chapter concludes with a summary of the review, discussing future research directions and the importance of community detection in understanding complex systems.The chapter "Community Detection in Graphs" by Santo Fortunato provides a comprehensive overview of the field of community detection in graphs, which is crucial for understanding complex systems. The main focus is on the organization of vertices into clusters, known as communities, where edges within clusters are more common than between clusters. These communities are analogous to tissues or organs in biological systems and play significant roles in various disciplines such as sociology, biology, and computer science. The chapter begins by introducing the concept of community structure in real-world networks, highlighting examples from social networks, protein-protein interaction networks, and technological networks. It emphasizes the importance of community detection in applications such as improving web services, customer segmentation, and efficient routing in ad hoc networks. The text then delves into the elements of community detection, including computational complexity, definitions of communities and partitions, and traditional methods like graph partitioning, hierarchical clustering, partitional clustering, and spectral clustering. It also discusses modern techniques such as divisive algorithms, modularity-based methods, spectral algorithms, dynamic algorithms, and methods based on statistical inference. The chapter explores the challenges and limitations of existing methods, particularly the issue of overlapping communities and the need for efficient algorithms to handle large networks. It provides a detailed discussion on the significance of clustering and the testing and comparison of algorithms. Finally, the chapter concludes with a summary of the review, discussing future research directions and the importance of community detection in understanding complex systems.