# Hypergraph clustering using Ricci curvature: an edge transport perspective

arXiv: https://arxiv.org/abs/2412.15695 · HTML: https://mlsanity.com/paper/2412.15695/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 60 references that are in the map.
- First posted on arXiv 20 Dec 2024.

## Builds on (most cited first, 30 of 30)

- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Deep Graph Contrastive Representation Learning](https://mlsanity.com/paper/2006.04131/) (2020)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [Community Detection and Stochastic Block Models](https://mlsanity.com/paper/1703.10146/) (2017)
- [Hyper-SAGNN: a self-attention based graph neural network for hypergraphs](https://mlsanity.com/paper/1911.02613/) (2019)
- [On Efficient Optimal Transport: An Analysis of Greedy and Accelerated Mirror Descent Algorithms](https://mlsanity.com/paper/1901.06482/) (2019)
- [Community Detection on Networks with Ricci Flow](https://mlsanity.com/paper/1907.03993/) (2019)
- [Random Walks on Hypergraphs with Edge-Dependent Vertex Weights](https://mlsanity.com/paper/1905.08287/) (2019)
- [CO-Optimal Transport](https://mlsanity.com/paper/2002.03731/) (2020)
- [The Total Variation on Hypergraphs - Learning on Hypergraphs Revisited](https://mlsanity.com/paper/1312.5179/) (2013)
- [Double-Scale Self-Supervised Hypergraph Learning for Group Recommendation](https://mlsanity.com/paper/2109.04200/) (2021)
- [The why, how, and when of representations for complex systems](https://mlsanity.com/paper/2006.02870/) (2020)
- [Ricci Curvature of the Internet Topology](https://mlsanity.com/paper/1501.04138/) (2015)
- [Semi-supervised Hypergraph Node Classification on Hypergraph Line Expansion](https://mlsanity.com/paper/2005.04843/) (2020)
- [Stochastic Block Model for Hypergraphs: Statistical limits and a semidefinite programming approach](https://mlsanity.com/paper/1807.02884/) (2018)
- [I'm Me, We're Us, and I'm Us: Tri-directional Contrastive Learning on Hypergraphs](https://mlsanity.com/paper/2206.04739/) (2022)
- [Hypergraph Random Walks, Laplacians, and Clustering](https://mlsanity.com/paper/2006.16377/) (2020)
- [Curvature-based Clustering on Graphs](https://mlsanity.com/paper/2307.10155/) (2023)
- [Euler Characteristic Tools For Topological Data Analysis](https://mlsanity.com/paper/2303.14040/) (2023)
- [More Recent Advances in (Hyper)Graph Partitioning](https://mlsanity.com/paper/2205.13202/) (2022)
- [Ollivier-Ricci Curvature for Hypergraphs: A Unified Framework](https://mlsanity.com/paper/2210.12048/) (2022)
- [Ollivier-Ricci curvature convergence in random geometric graphs](https://mlsanity.com/paper/2008.01209/) (2020)
- [Hypergraph Co-Optimal Transport: Metric and Categorical Properties](https://mlsanity.com/paper/2112.03904/) (2021)
- [Forman-Ricci Curvature for Hypergraphs](https://mlsanity.com/paper/1811.07825/) (2018)
- [HashNWalk: Hash and Random Walk Based Anomaly Detection in Hyperedge Streams](https://mlsanity.com/paper/2204.13822/) (2022)
- [Non-Euclidean Mixture Model for Social Network Embedding](https://mlsanity.com/paper/2411.04876/) (2024)
- [Modularity Based Community Detection in Hypergraphs](https://mlsanity.com/paper/2406.17556/) (2024)
- [Topological Simplifications of Hypergraphs](https://mlsanity.com/paper/2104.11214/) (2021)
- [FREIGHT: Fast Streaming Hypergraph Partitioning](https://mlsanity.com/paper/2302.06259/) (2023)

## Built on by (most cited first, 1 of 1)

- [A roadmap for curvature-based geometric data analysis and learning](https://mlsanity.com/paper/2510.22599/) (2025)

## Abstract (arXiv)

In this paper, we introduce a novel method for extending Ricci flow to hypergraphs by defining probability measures on the edges and transporting them on the line expansion. This approach yields a new weighting on the edges, which proves particularly effective for community detection. We extensively compare this method with a similar notion of Ricci flow defined on the clique expansion, demonstrating its enhanced sensitivity to the hypergraph structure, especially in the presence of large hyperedges. The two methods are complementary and together form a powerful and highly interpretable framework for community detection in hypergraphs.