# From Graphs to Hypergraphs: Hypergraph Projection and its Remediation

arXiv: https://arxiv.org/abs/2401.08519 · HTML: https://mlsanity.com/paper/2401.08519/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 60 references that are in the map.
- First posted on arXiv 16 Jan 2024.

## Builds on (most cited first, 6 of 6)

- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [HNHN: Hypergraph Networks with Hyperedge Neurons](https://mlsanity.com/paper/2006.12278/) (2020)
- [Hyper-SAGNN: a self-attention based graph neural network for hypergraphs](https://mlsanity.com/paper/1911.02613/) (2019)
- [Distance Encoding: Design Provably More Powerful Neural Networks for Graph Representation Learning](https://mlsanity.com/paper/2009.00142/) (2020)
- [Revisiting graph neural networks and distance encoding from a practical view](https://mlsanity.com/paper/2011.12228/) (2020)

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

- [Hypergraphs as Weighted Directed Self-Looped Graphs: Spectral Properties, Clustering, Cheeger Inequality](https://mlsanity.com/paper/2411.03331/) (2024)
- [Higher-Order Knowledge Representations for Agentic Scientific Reasoning](https://mlsanity.com/paper/2601.04878/) (2026)
- [HiTeC: Hierarchical Contrastive Learning on Text-Attributed Hypergraph with Semantic-Aware Augmentation](https://mlsanity.com/paper/2508.03104/) (2025)
- [Higher-order Structure Boosts Link Prediction on Temporal Graphs](https://mlsanity.com/paper/2505.15746/) (2025)
- [Multi-view Attention Fusion of Heterogeneous Hypergraph with Dynamic Behavioral Profiling for Personalized Learning Resource Recommendation](https://mlsanity.com/paper/2603.13310/) (2026)
- [MobileSAM2: Lightweight Segment Anything for Spatial Intelligence](https://mlsanity.com/paper/2607.12297/) (2026)

## Abstract (arXiv)

We study the implications of the modeling choice to use a graph, instead of a hypergraph, to represent real-world interconnected systems whose constituent relationships are of higher order by nature. Such a modeling choice typically involves an underlying projection process that maps the original hypergraph onto a graph, and is common in graph-based analysis. While hypergraph projection can potentially lead to loss of higher-order relations, there exists very limited studies on the consequences of doing so, as well as its remediation. This work fills this gap by doing two things: (1) we develop analysis based on graph and set theory, showing two ubiquitous patterns of hyperedges that are root to structural information loss in all hypergraph projections; we also quantify the combinatorial impossibility of recovering the lost higher-order structures if no extra help is provided; (2) we still seek to recover the lost higher-order structures in hypergraph projection, and in light of (1)'s findings we propose to relax the problem into a learning-based setting. Under this setting, we develop a learning-based hypergraph reconstruction method based on an important statistic of hyperedge distributions that we find. Our reconstruction method is evaluated on 8 real-world datasets under different settings, and exhibits consistently good performance. We also demonstrate benefits of the reconstructed hypergraphs via use cases of protein rankings and link predictions.