# Hypergraph Clustering Based on PageRank

arXiv: https://arxiv.org/abs/2006.08302 · HTML: https://mlsanity.com/paper/2006.08302/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2020.

## Built on by (most cited first, 15 of 15)

- [Equivariant Hypergraph Diffusion Neural Operators](https://mlsanity.com/paper/2207.06680/) (2022)
- [Local Hyper-Flow Diffusion](https://mlsanity.com/paper/2102.07945/) (2021)
- [High-order Multi-view Clustering for Generic Data](https://mlsanity.com/paper/2209.10838/) (2022)
- [Hypergraph-enhanced Dual Semi-supervised Graph Classification](https://mlsanity.com/paper/2405.04773/) (2024)
- [Local Algorithms for Finding Densely Connected Clusters](https://mlsanity.com/paper/2106.05245/) (2021)
- [A Versatile Framework for Attributed Network Clustering via K-Nearest Neighbor Augmentation](https://mlsanity.com/paper/2408.05459/) (2024)
- [DisenHCN: Disentangled Hypergraph Convolutional Networks for Spatiotemporal Activity Prediction](https://mlsanity.com/paper/2208.06794/) (2022)
- [Finding Bipartite Components in Hypergraphs](https://mlsanity.com/paper/2205.02771/) (2022)
- [Hypergraphs as Weighted Directed Self-Looped Graphs: Spectral Properties, Clustering, Cheeger Inequality](https://mlsanity.com/paper/2411.03331/) (2024)
- [Local Clustering on Complex Graphs and Complex Hypergraphs](https://mlsanity.com/paper/2412.03008/) (2024)
- [Spectral Toolkit of Algorithms for Graphs: Technical Report (1)](https://mlsanity.com/paper/2304.03170/) (2023)
- [Sparse Pedestrian Character Learning for Trajectory Prediction](https://mlsanity.com/paper/2311.15512/) (2023)
- [Modeling Edge-Specific Node Features through Co-Representation Neural Hypergraph Diffusion](https://mlsanity.com/paper/2405.14286/) (2024)
- [A flexible PageRank-based graph embedding framework closely related to spectral eigenvector embeddings](https://mlsanity.com/paper/2207.11321/) (2022)
- [On Learning the Structure of Clusters in Graphs](https://mlsanity.com/paper/2212.14345/) (2022)

## Abstract (arXiv)

A hypergraph is a useful combinatorial object to model ternary or higher-order relations among entities. Clustering hypergraphs is a fundamental task in network analysis. In this study, we develop two clustering algorithms based on personalized PageRank on hypergraphs. The first one is local in the sense that its goal is to find a tightly connected vertex set with a bounded volume including a specified vertex. The second one is global in the sense that its goal is to find a tightly connected vertex set. For both algorithms, we discuss theoretical guarantees on the conductance of the output vertex set. Also, we experimentally demonstrate that our clustering algorithms outperform existing methods in terms of both the solution quality and running time. To the best of our knowledge, ours are the first practical algorithms for hypergraphs with theoretical guarantees on the conductance of the output set.