# Hypergraph reconstruction from network data

arXiv: https://arxiv.org/abs/2008.04948 · HTML: https://mlsanity.com/paper/2008.04948/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Aug 2020.

## Built on by (most cited first, 18 of 18)

- [Hyper-YOLO: When Visual Object Detection Meets Hypergraph Computation](https://mlsanity.com/paper/2408.04804/) (2024)
- [Inference of hyperedges and overlapping communities in hypergraphs](https://mlsanity.com/paper/2204.05646/) (2022)
- [Learning Hypergraphs From Signals With Dual Smoothness Prior](https://mlsanity.com/paper/2211.01717/) (2022)
- [Disentangling homophily, community structure and triadic closure in networks](https://mlsanity.com/paper/2101.02510/) (2021)
- [A Markov Random Field model for Hypergraph-based Machine Learning](https://mlsanity.com/paper/2308.14172/) (2023)
- [Interaction Measures, Partition Lattices and Kernel Tests for High-Order Interactions](https://mlsanity.com/paper/2306.00904/) (2023)
- [Learning graphs and simplicial complexes from data](https://mlsanity.com/paper/2312.10545/) (2023)
- [Information-Theoretic Measures on Lattices for High-Order Interactions](https://mlsanity.com/paper/2408.07533/) (2024)
- [SPHINX: Structural Prediction using Hypergraph Inference Network](https://mlsanity.com/paper/2410.03208/) (2024)
- [Degree Heterogeneity in Higher-Order Networks: Inference in the Hypergraph boldsymbolβ-Model](https://mlsanity.com/paper/2307.02818/) (2023)
- [Symmetry-driven embedding of networks in hyperbolic space](https://mlsanity.com/paper/2406.10711/) (2024)
- [Higher-order Structure Boosts Link Prediction on Temporal Graphs](https://mlsanity.com/paper/2505.15746/) (2025)
- [Permutation-Free High-Order Interaction Tests](https://mlsanity.com/paper/2506.05963/) (2025)
- [Beyond Pairwise Connections: Extracting High-Order Functional Brain Network Structures under Global Constraints](https://mlsanity.com/paper/2510.09175/) (2025)
- [Supervised Hypergraph Reconstruction](https://mlsanity.com/paper/2211.13343/) (2022)
- [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)
- [MobileSAM2: Lightweight Segment Anything for Spatial Intelligence](https://mlsanity.com/paper/2607.12297/) (2026)

## Abstract (arXiv)

Networks can describe the structure of a wide variety of complex systems by specifying which pairs of entities in the system are connected. While such pairwise representations are flexible, they are not necessarily appropriate when the fundamental interactions involve more than two entities at the same time. Pairwise representations nonetheless remain ubiquitous, because higher-order interactions are often not recorded explicitly in network data. Here, we introduce a Bayesian approach to reconstruct latent higher-order interactions from ordinary pairwise network data. Our method is based on the principle of parsimony and only includes higher-order structures when there is sufficient statistical evidence for them. We demonstrate its applicability to a wide range of datasets, both synthetic and empirical.