# Topological Simplifications of Hypergraphs

arXiv: https://arxiv.org/abs/2104.11214 · HTML: https://mlsanity.com/paper/2104.11214/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Apr 2021.

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

- [Parameter Efficient Fine Tuning: A Comprehensive Analysis Across Applications](https://mlsanity.com/paper/2404.13506/) (2024)
- [Hypergraph clustering using Ricci curvature: an edge transport perspective](https://mlsanity.com/paper/2412.15695/) (2024)

## Abstract (arXiv)

We study hypergraph visualization via its topological simplification. We explore both vertex simplification and hyperedge simplification of hypergraphs using tools from topological data analysis. In particular, we transform a hypergraph to its graph representations known as the line graph and clique expansion. A topological simplification of such a graph representation induces a simplification of the hypergraph. In simplifying a hypergraph, we allow vertices to be combined if they belong to almost the same set of hyperedges, and hyperedges to be merged if they share almost the same set of vertices. Our proposed approaches are general, mathematically justifiable, and they put vertex simplification and hyperedge simplification in a unifying framework.