This study introduces the Lower Ricci Curvature (LRC), a novel, scalable, and scale-free discrete curvature designed to enhance community detection in networks. Addressing the computational challenges posed by existing curvature-based methods, LRC offers a streamlined approach with linear computational complexity, making it well-suited for large-scale network analysis. We further develop an LRC-based preprocessing method that effectively augments popular community detection algorithms. Through comprehensive simulations and applications on real-world datasets, including the NCAA football league network, the DBLP collaboration network, the Amazon product co-purchasing network, and the YouTube social network, we demonstrate the efficacy of our method in significantly improving the performance of various community detection algorithms.

翻译：本研究提出了一种新颖、可扩展且无标度的离散曲率——下里奇曲率（Lower Ricci Curvature，简称LRC），旨在增强网络中的社区检测能力。针对现有基于曲率的方法所面临的计算挑战，LRC提供了一种具有线性计算复杂度的简化方法，使其特别适用于大规模网络分析。我们进一步开发了一种基于LRC的预处理方法，能够有效增强流行的社区检测算法。通过在真实世界数据集（包括NCAA美式足球联赛网络、DBLP合作网络、亚马逊产品共同购买网络以及YouTube社交网络）上的全面仿真与应用，我们证明了该方法在显著提升多种社区检测算法性能方面的有效性。