  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.
