Beyond directed hypergraphs: heterogeneous hypergraphs and spectral centralities
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916370452578304 |
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| author | Contreras-Aso, Gonzalo Criado, Regino Romance, Miguel |
| author_facet | Contreras-Aso, Gonzalo Criado, Regino Romance, Miguel |
| contents | The study of hypergraphs has received a lot of attention over the past few years, however up until recently there has been no interest in systems where higher order interactions are not undirected. In this article we introduce the notion of heterogeneous hypergraphs from an algebraic point of view, which have traditional directed hypergraphs as a particular case. We furthermore analytically study the spectral centralities associated to some types of heterogeneous hypergraphs, extending previously defined eigenvector-like centrality measures to this new realm. We supplement the analytical arguments with some numerical comparisons of pairwise and higher order rankings, and we construct directed higher order networks from real data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_11825 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Beyond directed hypergraphs: heterogeneous hypergraphs and spectral centralities Contreras-Aso, Gonzalo Criado, Regino Romance, Miguel Mathematical Physics Spectral Theory The study of hypergraphs has received a lot of attention over the past few years, however up until recently there has been no interest in systems where higher order interactions are not undirected. In this article we introduce the notion of heterogeneous hypergraphs from an algebraic point of view, which have traditional directed hypergraphs as a particular case. We furthermore analytically study the spectral centralities associated to some types of heterogeneous hypergraphs, extending previously defined eigenvector-like centrality measures to this new realm. We supplement the analytical arguments with some numerical comparisons of pairwise and higher order rankings, and we construct directed higher order networks from real data. |
| title | Beyond directed hypergraphs: heterogeneous hypergraphs and spectral centralities |
| topic | Mathematical Physics Spectral Theory |
| url | https://arxiv.org/abs/2403.11825 |