Discrete scalar curvature as a weighted sum of Ollivier-Ricci curvatures
Not on the map. Why?
Abstract (arXiv)
We study the relationship between discrete analogues of Ricci and scalar curvature that are defined for point clouds and graphs. In the discrete setting, Ricci curvature is replaced by Ollivier-Ricci curvature. Scalar curvature can be computed as the trace of Ricci curvature for a Riemannian manifold; this motivates a new definition of a scalar version of Ollivier-Ricci curvature. We show that our definition converges to scalar curvature for nearest neighbor graphs obtained by sampling from a manifold. We also prove some new results about the convergence of Ollivier-Ricci curvature to Ricci curvature.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 9 of its 22 references that are in the map. First posted on arXiv 6 Oct 2025.
Builds on
9 of 22 references.
References · 9
- 2022Revisiting Over-smoothing and Over-squashing Using Ollivier-Ricci Curvaturecited by 98
- 2018Error estimates for spectral convergence of the graph Laplacian on random geometric graphs towards the Laplace--Beltrami operatorcited by 70
- 2019Community Detection on Networks with Ricci Flowcited by 62
- 2023Curvature Filtrations for Graph Generative Model Evaluationcited by 19
- 2023Effective Structural Encodings via Local Curvature Profilescited by 13
- 2020Ollivier-Ricci curvature convergence in random geometric graphscited by 11
- 2023Continuum Limits of Ollivier's Ricci Curvature on data clouds: pointwise consistency and global lower boundscited by 6
- 2024Recovering Manifold Structure Using Ollivier-Ricci Curvaturecited by 6
- 2025EmbedOR: Provable Cluster-Preserving Visualizations with Curvature-Based Stochastic Neighbor Embeddingscited by 2
Built on by
Citing papers per year: 2025: 1.
1 paper.