# Hypernetwork Science via High-Order Hypergraph Walks

arXiv: https://arxiv.org/abs/1906.11295 · HTML: https://mlsanity.com/paper/1906.11295/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jun 2019.

## Built on by (most cited first, 20 of 20)

- [Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond](https://mlsanity.com/paper/2101.05510/) (2021)
- [Hypergraph Convolutional Networks via Equivalency between Hypergraphs and Undirected Graphs](https://mlsanity.com/paper/2203.16939/) (2022)
- [Ollivier-Ricci Curvature for Hypergraphs: A Unified Framework](https://mlsanity.com/paper/2210.12048/) (2022)
- [HYGENE: A Diffusion-based Hypergraph Generation Method](https://mlsanity.com/paper/2408.16457/) (2024)
- [The SVD of Convolutional Weights: A CNN Interpretability Framework](https://mlsanity.com/paper/2208.06894/) (2022)
- [CAT-Walk: Inductive Hypergraph Learning via Set Walks](https://mlsanity.com/paper/2306.11147/) (2023)
- [Sparse random hypergraphs: Non-backtracking spectra and community detection](https://mlsanity.com/paper/2203.07346/) (2022)
- [Demystifying Higher-Order Graph Neural Networks](https://mlsanity.com/paper/2406.12841/) (2024)
- [HyperMagNet: A Magnetic Laplacian based Hypergraph Neural Network](https://mlsanity.com/paper/2402.09676/) (2024)
- [All the World's a (Hyper)Graph: A Data Drama](https://mlsanity.com/paper/2206.08225/) (2022)
- [A Hypergraph-Based Machine Learning Ensemble Network Intrusion Detection System](https://mlsanity.com/paper/2211.03933/) (2022)
- [HiTeC: Hierarchical Contrastive Learning on Text-Attributed Hypergraph with Semantic-Aware Augmentation](https://mlsanity.com/paper/2508.03104/) (2025)
- [BHyGNN+: Unsupervised Representation Learning for Heterophilic Hypergraphs](https://mlsanity.com/paper/2602.14919/) (2026)
- [Hypergraph Dissimilarity Measures](https://mlsanity.com/paper/2106.08206/) (2021)
- [Scalable tensor methods for nonuniform hypergraphs](https://mlsanity.com/paper/2306.17825/) (2023)
- [Scalable Hypergraph Structure Learning with Diverse Smoothness Priors](https://mlsanity.com/paper/2504.03583/) (2025)
- [Entity Graph Extraction from Legal Acts -- a Prototype for a Use Case in Policy Design Analysis](https://mlsanity.com/paper/2209.00944/) (2022)
- [Automating the Analysis of Institutional Design in International Agreements](https://mlsanity.com/paper/2305.16750/) (2023)
- [Characterizing User Archetypes and Discussions on Scored.co](https://mlsanity.com/paper/2407.21753/) (2024)
- [Feature-Aware (Hyper)graph Generation via Next-Scale Prediction](https://mlsanity.com/paper/2506.01467/) (2025)

## Abstract (arXiv)

We propose high-order hypergraph walks as a framework to generalize graph-based network science techniques to hypergraphs. Edge incidence in hypergraphs is quantitative, yielding hypergraph walks with both length and width. Graph methods which then generalize to hypergraphs include connected component analyses, graph distance-based metrics such as closeness centrality, and motif-based measures such as clustering coefficients. We apply high-order analogs of these methods to real world hypernetworks, and show they reveal nuanced and interpretable structure that cannot be detected by graph-based methods. Lastly, we apply three generative models to the data and find that basic hypergraph properties, such as density and degree distributions, do not necessarily control these new structural measurements. Our work demonstrates how analyses of hypergraph-structured data are richer when utilizing tools tailored to capture hypergraph-native phenomena, and suggests one possible avenue towards that end.