# Tensor Entropy for Uniform Hypergraphs

arXiv: https://arxiv.org/abs/1912.09624 · HTML: https://mlsanity.com/paper/1912.09624/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Dec 2019.

## Built on by (most cited first, 4 of 4)

- [A Survey on Hyperlink Prediction](https://mlsanity.com/paper/2207.02911/) (2022)
- [Hypergraph Dissimilarity Measures](https://mlsanity.com/paper/2106.08206/) (2021)
- [Lower Ricci Curvature for Hypergraphs](https://mlsanity.com/paper/2506.03943/) (2025)
- [Beyond Distance: Quantifying Point Cloud Dynamics with Persistent Homology and Dynamic Optimal Transport](https://mlsanity.com/paper/2603.15683/) (2026)

## Abstract (arXiv)

In this paper, we develop the notion of entropy for uniform hypergraphs via tensor theory. We employ the probability distribution of the generalized singular values, calculated from the higher-order singular value decomposition of the Laplacian tensors, to fit into the Shannon entropy formula. We show that this tensor entropy is an extension of von Neumann entropy for graphs. In addition, we establish results on the lower and upper bounds of the entropy and demonstrate that it is a measure of regularity for uniform hypergraphs in simulated and experimental data. We exploit the tensor train decomposition in computing the proposed tensor entropy efficiently. Finally, we introduce the notion of robustness for uniform hypergraphs.