# Curvature of Hypergraphs via Multi-Marginal Optimal Transport

arXiv: https://arxiv.org/abs/1803.08584 · HTML: https://mlsanity.com/paper/1803.08584/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Mar 2018.

## Built on by (most cited first, 3 of 3)

- [Ollivier-Ricci Curvature for Hypergraphs: A Unified Framework](https://mlsanity.com/paper/2210.12048/) (2022)
- [Accelerated Evaluation of Ollivier-Ricci Curvature Lower Bounds: Bridging Theory and Computation](https://mlsanity.com/paper/2405.13302/) (2024)
- [A roadmap for curvature-based geometric data analysis and learning](https://mlsanity.com/paper/2510.22599/) (2025)

## Abstract (arXiv)

We introduce a novel definition of curvature for hypergraphs, a natural generalization of graphs, by introducing a multi-marginal optimal transport problem for a naturally defined random walk on the hypergraph. This curvature, termed coarse scalar curvature, generalizes a recent definition of Ricci curvature for Markov chains on metric spaces by Ollivier [Journal of Functional Analysis 256 (2009) 810-864], and is related to the scalar curvature when the hypergraph arises naturally from a Riemannian manifold. We investigate basic properties of the coarse scalar curvature and obtain several bounds. Empirical experiments indicate that coarse scalar curvatures are capable of detecting "bridges" across connected components in hypergraphs, suggesting it is an appropriate generalization of curvature on simple graphs.