# How Do Hyperedges Overlap in Real-World Hypergraphs? -- Patterns, Measures, and Generators

arXiv: https://arxiv.org/abs/2101.07480 · HTML: https://mlsanity.com/paper/2101.07480/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jan 2021.

## Built on by (most cited first, 22 of 22)

- [Equivariant Hypergraph Diffusion Neural Operators](https://mlsanity.com/paper/2207.06680/) (2022)
- [A Survey on Hypergraph Neural Networks: An In-Depth and Step-By-Step Guide](https://mlsanity.com/paper/2404.01039/) (2024)
- [Classification of Edge-dependent Labels of Nodes in Hypergraphs](https://mlsanity.com/paper/2306.03032/) (2023)
- [AHP: Learning to Negative Sample for Hyperedge Prediction](https://mlsanity.com/paper/2204.06353/) (2022)
- [Hypergraph Artificial Benchmark for Community Detection (h-ABCD)](https://mlsanity.com/paper/2210.15009/) (2022)
- [CHGNN: A Semi-Supervised Contrastive Hypergraph Learning Network](https://mlsanity.com/paper/2303.06213/) (2023)
- [Modularity Based Community Detection in Hypergraphs](https://mlsanity.com/paper/2406.17556/) (2024)
- [Generalization Performance of Hypergraph Neural Networks](https://mlsanity.com/paper/2501.12554/) (2025)
- [HyperGALE: ASD Classification via Hypergraph Gated Attention with Learnable Hyperedges](https://mlsanity.com/paper/2403.14484/) (2024)
- [Modeling Hypergraph Using Large Language Models](https://mlsanity.com/paper/2510.11728/) (2025)
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- [Using Graph Neural Networks for Program Termination](https://mlsanity.com/paper/2207.14648/) (2022)
- [Tribe or Not? Critical Inspection of Group Differences Using TribalGram](https://mlsanity.com/paper/2303.09664/) (2023)
- [Edge Probability Graph Models Beyond Edge Independency: Concepts, Analyses, and Algorithms](https://mlsanity.com/paper/2405.16726/) (2024)
- [Overlap-aware meta-learning attention to enhance hypergraph neural networks for node classification](https://mlsanity.com/paper/2503.07961/) (2025)
- [MARIOH: Multiplicity-Aware Hypergraph Reconstruction](https://mlsanity.com/paper/2504.00522/) (2025)
- [Learning Multi-Order Block Structure in Higher-Order Networks](https://mlsanity.com/paper/2511.21350/) (2025)

## Abstract (arXiv)

Hypergraphs, a generalization of graphs, naturally represent groupwise relationships among multiple individuals or objects, which are common in many application areas, including web, bioinformatics, and social networks. The flexibility in the number of nodes in each hyperedge, which provides the expressiveness of hypergraphs, brings about structural differences between graphs and hypergraphs. Especially, the overlaps of hyperedges lead to complex high-order relations beyond pairwise relations, raising new questions that have not been considered in graphs: How do hyperedges overlap in real-world hypergraphs? Are there any pervasive characteristics? What underlying process can cause such patterns? In this work, we closely investigate thirteen real-world hypergraphs from various domains and share interesting observations of overlaps of hyperedges. To this end, we define principled measures and statistically compare the overlaps of hyperedges in real-world hypergraphs and those in null models. Additionally, based on the observations, we propose HyperLap, a realistic hypergraph generative model. HyperLap is (a) Realistic: it accurately reproduces overlapping patterns of real-world hypergraphs, (b) Automatically Fittable: its parameters can be tuned automatically using HyperLap+ to generate hypergraphs particularly similar to a given target hypergraph, (c) Scalable: it generates and fits a hypergraph with 0.7 billion hyperedges within a few hours.