# Learning the effective order of a hypergraph dynamical system

arXiv: https://arxiv.org/abs/2306.01813 · HTML: https://mlsanity.com/paper/2306.01813/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 52 references that are in the map.
- First posted on arXiv 2 Jun 2023.

## Builds on (most cited first, 19 of 19)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Graph Neural Ordinary Differential Equations](https://mlsanity.com/paper/1911.07532/) (2019)
- [Networks beyond pairwise interactions: structure and dynamics](https://mlsanity.com/paper/2006.01764/) (2020)
- [What are higher-order networks?](https://mlsanity.com/paper/2104.11329/) (2021)
- [Contact patterns in a high school: a comparison between data collected using wearable sensors, contact diaries and friendship surveys](https://mlsanity.com/paper/1506.03645/) (2015)
- [Generative hypergraph clustering: from blockmodels to modularity](https://mlsanity.com/paper/2101.09611/) (2021)
- [Random Walks on Hypergraphs with Edge-Dependent Vertex Weights](https://mlsanity.com/paper/1905.08287/) (2019)
- [Neural Dynamics on Complex Networks](https://mlsanity.com/paper/1908.06491/) (2019)
- [Hierarchical Hyperedge Embedding-based Representation Learning for Group Recommendation](https://mlsanity.com/paper/2103.13506/) (2021)
- [Random walks on hypergraphs](https://mlsanity.com/paper/1911.06523/) (2019)
- [Hypergraph Cuts with General Splitting Functions](https://mlsanity.com/paper/2001.02817/) (2020)
- [Strongly Local Hypergraph Diffusions for Clustering and Semi-supervised Learning](https://mlsanity.com/paper/2011.07752/) (2020)
- [Dynamics on higher-order networks: A review](https://mlsanity.com/paper/2203.06601/) (2022)
- [Local Hyper-Flow Diffusion](https://mlsanity.com/paper/2102.07945/) (2021)
- [Epidemics on Hypergraphs: Spectral Thresholds for Extinction](https://mlsanity.com/paper/2103.07319/) (2021)
- [Core-periphery detection in hypergraphs](https://mlsanity.com/paper/2202.12769/) (2022)
- [Modelling Non-Linear Consensus Dynamics on Hypergraphs](https://mlsanity.com/paper/2007.09391/) (2020)
- [A Bounded-Confidence Model of Opinion Dynamics on Hypergraphs](https://mlsanity.com/paper/2102.06825/) (2021)
- [Consensus Dynamics and Opinion Formation on Hypergraphs](https://mlsanity.com/paper/2105.01369/) (2021)

## Built on by (most cited first, 3 of 3)

- [Knowledge Is Not Static: Order-Aware Hypergraph RAG for Language Models](https://mlsanity.com/paper/2604.12185/) (2026)
- [Graph Neural Networks Based Analog Circuit Link Prediction](https://mlsanity.com/paper/2504.10240/) (2025)
- [Learning Multi-Order Block Structure in Higher-Order Networks](https://mlsanity.com/paper/2511.21350/) (2025)

## Abstract (arXiv)

Dynamical systems on hypergraphs can display a rich set of behaviours not observable for systems with pairwise interactions. Given a distributed dynamical system with a putative hypergraph structure, an interesting question is thus how much of this hypergraph structure is actually necessary to faithfully replicate the observed dynamical behaviour. To answer this question, we propose a method to determine the minimum order of a hypergraph necessary to approximate the corresponding dynamics accurately. Specifically, we develop an analytical framework that allows us to determine this order when the type of dynamics is known. We utilize these ideas in conjunction with a hypergraph neural network to directly learn the dynamics itself and the resulting order of the hypergraph from both synthetic and real data sets consisting of observed system trajectories.