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.

翻译：图曲率的概念最近在网络研究领域受到关注，其中奥利维耶-里奇曲率（ORC）尤其被用于网络分析中的多项任务，例如社区检测。在本研究中，我们采用不同方法，探讨了由福尔曼提出的里奇曲率离散化增强形式（AFRC）。我们从实证与理论两方面研究了其与ORC及未增强的福尔曼-里奇曲率的关系。特别地，我们证明AFRC通常能提供足够深入理解网络结构的视角，可用于社区检测，从而为先前基于ORC的方法提供了计算成本更低的替代方案。我们提出的新型基于AFRC的社区检测算法与基于ORC的方法具有可比性。