Geometric characterisation of structural and regular equivalences in undirected (hyper)graphs
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914228541063168 |
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| author | Eidi, Marzieh Otter, Nina |
| author_facet | Eidi, Marzieh Otter, Nina |
| contents | Similarity notions between vertices in a graph, such as structural and regular equivalence, are one of the main ingredients in clustering tools in complex network science. We generalise structural and regular equivalences for undirected hypergraphs and provide a characterisation of structural and regular equivalences of undirected graphs and hypergraphs through neighbourhood graphs and Ollivier-Ricci curvature. Our characterisation sheds new light on these similarity notions opening a new avenue for their exploration. These characterisations also enable the construction of a possibly wide family of regular partitions, thereby offering a new route to a task that has so far been computationally challenging. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24961 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometric characterisation of structural and regular equivalences in undirected (hyper)graphs Eidi, Marzieh Otter, Nina Combinatorics Discrete Mathematics Social and Information Networks Similarity notions between vertices in a graph, such as structural and regular equivalence, are one of the main ingredients in clustering tools in complex network science. We generalise structural and regular equivalences for undirected hypergraphs and provide a characterisation of structural and regular equivalences of undirected graphs and hypergraphs through neighbourhood graphs and Ollivier-Ricci curvature. Our characterisation sheds new light on these similarity notions opening a new avenue for their exploration. These characterisations also enable the construction of a possibly wide family of regular partitions, thereby offering a new route to a task that has so far been computationally challenging. |
| title | Geometric characterisation of structural and regular equivalences in undirected (hyper)graphs |
| topic | Combinatorics Discrete Mathematics Social and Information Networks |
| url | https://arxiv.org/abs/2512.24961 |