# Hypergraph Laplacians in Diffusion Framework

arXiv: https://arxiv.org/abs/2102.08867 · HTML: https://mlsanity.com/paper/2102.08867/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Feb 2021.

## Built on by (most cited first, 2 of 2)

- [HyGNN: Drug-Drug Interaction Prediction via Hypergraph Neural Network](https://mlsanity.com/paper/2206.12747/) (2022)
- [Seq-HyGAN: Sequence Classification via Hypergraph Attention Network](https://mlsanity.com/paper/2303.02393/) (2023)

## Abstract (arXiv)

Networks are important structures used to model complex systems where interactions take place. In a basic network model, entities are represented as nodes, and interaction and relations among them are represented as edges. However, in a complex system, we cannot describe all relations as pairwise interactions, rather should describe as higher-order interactions. Hypergraphs are successfully used to model higher-order interactions in complex systems. In this paper, we present two new hypergraph Laplacians based on diffusion framework. Our Laplacians take the relations between higher-order interactions into consideration, hence can be used to model diffusion on hypergraphs not only between vertices but also higher-order structures. These Laplacians can be employed in different network mining problems on hypergraphs, such as social contagion models on hypergraphs, influence study on hypergraphs, and hypergraph classification, to list a few.