Exploring the Non-uniqueness of Node Co-occurrence Matrices of Hypergraphs
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913903267545088 |
|---|---|
| author | LaRock, Timothy Lambiotte, Renaud |
| author_facet | LaRock, Timothy Lambiotte, Renaud |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_01479 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exploring the Non-uniqueness of Node Co-occurrence Matrices of Hypergraphs LaRock, Timothy Lambiotte, Renaud Social and Information Networks Physics and Society 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. |
| title | Exploring the Non-uniqueness of Node Co-occurrence Matrices of Hypergraphs |
| topic | Social and Information Networks Physics and Society |
| url | https://arxiv.org/abs/2506.01479 |