# Exploring the Non-uniqueness of Node Co-occurrence Matrices of Hypergraphs

arXiv: https://arxiv.org/abs/2506.01479 · HTML: https://mlsanity.com/paper/2506.01479/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jun 2025.

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

- [Do Higher-Order Models Win for Higher-Order Reasons? Rethinking Performance Gains in Hypergraph Learning](https://mlsanity.com/paper/2610.07981/) (2026)

## Abstract (arXiv)

Hypergraphs extend traditional networks by capturing multi-way or group interactions. Given the complexity of hypergraph data and the wide range of methodology available for pairwise network analysis, hypergraph data is often projected onto a weighted and undirected network. The simplest of these projections, often referred to as a node co-occurrence matrix, is known to be non-unique, as distinct non-isomorphic hypergraphs can produce the same weighted adjacency matrix. This non-uniqueness raises important questions about the structural information lost during the projection and how to efficiently quantify the complexity of the original hypergraph. Here we develop a search algorithm to identify all hypergraphs corresponding to a given projection, analyze its runtime, and explore its parallelisability. Applying this algorithm to projections derived from a random hypergraph model, we characterize conditions under which projections are non-unique. Our findings provide a new framework and set of computational tools to investigate projections of hypergraphs.