# Structural Patterns and Generative Models of Real-world Hypergraphs

arXiv: https://arxiv.org/abs/2006.07060 · HTML: https://mlsanity.com/paper/2006.07060/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2020.

## Built on by (most cited first, 29 of 29)

- [A Survey on Hypergraph Neural Networks: An In-Depth and Step-By-Step Guide](https://mlsanity.com/paper/2404.01039/) (2024)
- [I'm Me, We're Us, and I'm Us: Tri-directional Contrastive Learning on Hypergraphs](https://mlsanity.com/paper/2206.04739/) (2022)
- [Classification of Edge-dependent Labels of Nodes in Hypergraphs](https://mlsanity.com/paper/2306.03032/) (2023)
- [Neural Predicting Higher-order Patterns in Temporal Networks](https://mlsanity.com/paper/2106.06039/) (2021)
- [AHP: Learning to Negative Sample for Hyperedge Prediction](https://mlsanity.com/paper/2204.06353/) (2022)
- [Ollivier-Ricci Curvature for Hypergraphs: A Unified Framework](https://mlsanity.com/paper/2210.12048/) (2022)
- [Learning High-Order Relationships of Brain Regions](https://mlsanity.com/paper/2312.02203/) (2023)
- [Hypergraph Artificial Benchmark for Community Detection (h-ABCD)](https://mlsanity.com/paper/2210.15009/) (2022)
- [Learning Hypergraphs From Signals With Dual Smoothness Prior](https://mlsanity.com/paper/2211.01717/) (2022)
- [HYGENE: A Diffusion-based Hypergraph Generation Method](https://mlsanity.com/paper/2408.16457/) (2024)
- [A Markov Random Field model for Hypergraph-based Machine Learning](https://mlsanity.com/paper/2308.14172/) (2023)
- [What Do LLMs Need to Understand Graphs: A Survey of Parametric Representation of Graphs](https://mlsanity.com/paper/2410.12126/) (2024)
- [Enhancing Hyperedge Prediction with Context-Aware Self-Supervised Learning](https://mlsanity.com/paper/2309.05798/) (2023)
- [Generalization Performance of Hypergraph Neural Networks](https://mlsanity.com/paper/2501.12554/) (2025)
- [Deploying Models to Non-participating Clients in Federated Learning without Fine-tuning: A Hypernetwork-based Approach](https://mlsanity.com/paper/2508.12673/) (2025)
- [Hypernetwork Dismantling via Deep Reinforcement Learning](https://mlsanity.com/paper/2104.14332/) (2021)
- [Modeling Hypergraph Using Large Language Models](https://mlsanity.com/paper/2510.11728/) (2025)
- [SINGA-Easy: An Easy-to-Use Framework for MultiModal Analysis](https://mlsanity.com/paper/2108.02572/) (2021)
- [VisualTextRank: Unsupervised Graph-based Content Extraction for Automating Ad Text to Image Search](https://mlsanity.com/paper/2108.02725/) (2021)
- [Text is NOT Enough: Integrating Visual Impressions into Open-domain Dialogue Generation](https://mlsanity.com/paper/2109.05778/) (2021)
- [Discovering Personalized Semantics for Soft Attributes in Recommender Systems using Concept Activation Vectors](https://mlsanity.com/paper/2202.02830/) (2022)
- [Reinforced MOOCs Concept Recommendation in Heterogeneous Information Networks](https://mlsanity.com/paper/2203.11011/) (2022)
- [Explanation-Guided Fairness Testing through Genetic Algorithm](https://mlsanity.com/paper/2205.08335/) (2022)
- [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)
- [Feature-Aware (Hyper)graph Generation via Next-Scale Prediction](https://mlsanity.com/paper/2506.01467/) (2025)
- [Hypergraph Generation via Structured Stochastic Diffusion](https://mlsanity.com/paper/2605.05024/) (2026)
- [Anchor-guided Hypergraph Condensation with Dual-level Discrimination](https://mlsanity.com/paper/2605.10001/) (2026)
- [TAHB: A Comprehensive Benchmark for Text-Attributed Hypergraph Learning](https://mlsanity.com/paper/2608.15055/) (2026)

## Abstract (arXiv)

Graphs have been utilized as a powerful tool to model pairwise relationships between people or objects. Such structure is a special type of a broader concept referred to as hypergraph, in which each hyperedge may consist of an arbitrary number of nodes, rather than just two. A large number of real-world datasets are of this form - for example, list of recipients of emails sent from an organization, users participating in a discussion thread or subject labels tagged in an online question. However, due to complex representations and lack of adequate tools, little attention has been paid to exploring the underlying patterns in these interactions. In this work, we empirically study a number of real-world hypergraph datasets across various domains. In order to enable thorough investigations, we introduce the multi-level decomposition method, which represents each hypergraph by a set of pairwise graphs. Each pairwise graph, which we refer to as a k-level decomposed graph, captures the interactions between pairs of subsets of k nodes. We empirically find that at each decomposition level, the investigated hypergraphs obey five structural properties. These properties serve as criteria for evaluating how realistic a hypergraph is, and establish a foundation for the hypergraph generation problem. We also propose a hypergraph generator that is remarkably simple but capable of fulfilling these evaluation metrics, which are hardly achieved by other baseline generator models.