# Structural Controllability of Large-Scale Hypergraphs

arXiv: https://arxiv.org/abs/2603.19955 · HTML: https://mlsanity.com/paper/2603.19955/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 55 references that are in the map.
- First posted on arXiv 20 Mar 2026.

## Builds on (most cited first, 12 of 12)

- [Higher-order organization of complex networks](https://mlsanity.com/paper/1612.08447/) (2016)
- [What are higher-order networks?](https://mlsanity.com/paper/2104.11329/) (2021)
- [Epidemics on Hypergraphs: Spectral Thresholds for Extinction](https://mlsanity.com/paper/2103.07319/) (2021)
- [Explicit Solutions and Stability Properties of Homogeneous Polynomial Dynamical Systems](https://mlsanity.com/paper/2107.11438/) (2021)
- [Using Node Centrality and Optimal Control to Maximize Information Diffusion in Social Networks](https://mlsanity.com/paper/1602.01003/) (2016)
- [On Structural Controllability of Symmetric (Brain) Networks](https://mlsanity.com/paper/1706.05120/) (2017)
- [Observability of Hypergraphs](https://mlsanity.com/paper/2304.04883/) (2023)
- [On Metzler positive systems on hypergraphs](https://mlsanity.com/paper/2401.03652/) (2024)
- [On discrete-time polynomial dynamical systems on hypergraphs](https://mlsanity.com/paper/2403.03416/) (2024)
- [Global and local observability of hypergraphs](https://mlsanity.com/paper/2405.18969/) (2024)
- [Controllability and Observability of Temporal Hypergraphs](https://mlsanity.com/paper/2408.12085/) (2024)
- [Model Reduction of Homogeneous Polynomial Dynamical Systems via Tensor Decomposition](https://mlsanity.com/paper/2506.19165/) (2025)

## Abstract (arXiv)

Controlling real-world networked systems, including ecological, biomedical, and engineered networks that exhibit higher-order interactions, remains challenging due to inherent nonlinearities and large system scales. Despite extensive studies on graph controllability, the controllability properties of hypergraphs remain largely underdeveloped. Existing results focus primarily on exact controllability, which is often impractical for large-scale hypergraphs. In this article, we develop a structural controllability framework for hypergraphs by modeling hypergraph dynamics as polynomial dynamical systems. In particular, we extend classical notions of accessibility and dilation from linear graph-based systems to polynomial hypergraph dynamics and establish a hypergraph-based criterion under which the topology guarantees satisfaction of classical Lie-algebraic and Kalman-type rank conditions for almost all parameter choices. We further derive a topology-based lower bound on the minimum number of driver nodes required for structural controllability and leverage this bound to design a scalable driver node selection algorithm combining dilation-aware initialization via maximum matching with greedy accessibility expansion. We demonstrate the effectiveness and scalability of the proposed framework through numerical experiments on hypergraphs with tens to thousands of nodes and higher-order interactions.