# Forman's Ricci curvature - From networks to hypernetworks

arXiv: https://arxiv.org/abs/1810.07749 · HTML: https://mlsanity.com/paper/1810.07749/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Oct 2018.

## Built on by (most cited first, 6 of 6)

- [Curvature-based Clustering on Graphs](https://mlsanity.com/paper/2307.10155/) (2023)
- [Ollivier-Ricci Curvature for Hypergraphs: A Unified Framework](https://mlsanity.com/paper/2210.12048/) (2022)
- [Curvature-enhanced Graph Convolutional Network for Biomolecular Interaction Prediction](https://mlsanity.com/paper/2306.13699/) (2023)
- [Enhancing the Utility of Higher-Order Information in Relational Learning](https://mlsanity.com/paper/2502.09570/) (2025)
- [A roadmap for curvature-based geometric data analysis and learning](https://mlsanity.com/paper/2510.22599/) (2025)
- [Sandpile Economics: Theory, Identification, and Evidence](https://mlsanity.com/paper/2604.13890/) (2026)

## Abstract (arXiv)

Networks and their higher order generalizations, such as hypernetworks or multiplex networks are ever more popular models in the applied sciences. However, methods developed for the study of their structural properties go little beyond the common name and the heavy reliance of combinatorial tools. We show that, in fact, a geometric unifying approach is possible, by viewing them as polyhedral complexes endowed with a simple, yet, the powerful notion of curvature - the Forman Ricci curvature. We systematically explore some aspects related to the modeling of weighted and directed hypernetworks and present expressive and natural choices involved in their definitions. A benefit of this approach is a simple method of structure-preserving embedding of hypernetworks in Euclidean N-space. Furthermore, we introduce a simple and efficient manner of computing the well established Ollivier-Ricci curvature of a hypernetwork.