# Global and local observability of hypergraphs

arXiv: https://arxiv.org/abs/2405.18969 · HTML: https://mlsanity.com/paper/2405.18969/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2024.

## Built on by (most cited first, 1 of 1)

- [Structural Controllability of Large-Scale Hypergraphs](https://mlsanity.com/paper/2603.19955/) (2026)

## Abstract (arXiv)

This paper studies observability for non-uniform hypergraphs with inputs and outputs. To capture higher-order interactions, we define a canonical non-homogeneous dynamical system with nonlinear outputs on hypergraphs. We then construct algebraic necessary and sufficient conditions based on polynomial ideals and varieties for global observability at an initial state of hypergraphs. An example is given to illustrate the proposed criteria for observability. Further, necessary and sufficient conditions for local observability are derived based on rank conditions of observability matrices, which provide a framework to study local observability for non-uniform hypergraphs. Finally, the similarity of observability for hypergraphs is proposed using similarity of tensors, which reveals the relation of observability between two hypergraphs and helps to check the observability intuitively.