The paper addresses the challenge of defining and identifying communities in networks, which is crucial for various domains such as social tasks, biological inquiries, and technological problems. The authors propose a new local algorithm to detect communities that outperforms existing algorithms in terms of computational cost while maintaining reliability. They introduce quantitative definitions of communities to make existing algorithms self-contained and provide a detailed comparison with the Girvan-Newman (GN) algorithm. The new algorithm is tested on artificial and real-world graphs, including a network of scientific collaborations, demonstrating its effectiveness in large-scale systems. The paper also discusses the limitations of the GN algorithm and the potential of the new algorithm in analyzing disassortative networks. Overall, the work contributes to the field by providing a more efficient and accurate method for community detection in complex networks.The paper addresses the challenge of defining and identifying communities in networks, which is crucial for various domains such as social tasks, biological inquiries, and technological problems. The authors propose a new local algorithm to detect communities that outperforms existing algorithms in terms of computational cost while maintaining reliability. They introduce quantitative definitions of communities to make existing algorithms self-contained and provide a detailed comparison with the Girvan-Newman (GN) algorithm. The new algorithm is tested on artificial and real-world graphs, including a network of scientific collaborations, demonstrating its effectiveness in large-scale systems. The paper also discusses the limitations of the GN algorithm and the potential of the new algorithm in analyzing disassortative networks. Overall, the work contributes to the field by providing a more efficient and accurate method for community detection in complex networks.