The notion of curvature on graphs has recently gained traction in the networks community, with the Ollivier-Ricci curvature (ORC) in particular being used for several tasks in network analysis, such as community detection. In this work, we choose a different approach and study augmentations of the discretization of the Ricci curvature proposed by Forman (AFRC). We empirically and theoretically investigate its relation to the ORC and the un-augmented Forman-Ricci curvature. In particular, we provide evidence that the AFRC frequently gives sufficient insight into the structure of a network to be used for community detection, and therefore provides a computationally cheaper alternative to previous ORC-based methods. Our novel AFRC-based community detection algorithm is competitive with an ORC-based approach. The codebase for fast and efficient computations of AFRC and the experiments in this article will be made publicly available upon publication.

翻译：图上的曲率概念近来在网络社区中备受关注，其中Ollivier-Ricci曲率（ORC）尤其被用于网络分析中的若干任务，例如社区检测。在本文中，我们采取不同的方法，研究Forman提出的里奇曲率离散化形式的增强（AFRC）。我们从经验与理论层面探究其与ORC及未增强的Forman-Ricci曲率之间的关系。特别是，我们提供证据表明，AFRC通常能为用于社区检测的网络结构提供足够的洞察，因此为以往基于ORC的方法提供了一种计算成本更低的替代方案。我们基于AFRC的新型社区检测算法与基于ORC的方法相比具有竞争力。用于快速高效计算AFRC的代码库以及本文的实验结果将在出版后公开。