{"ID":2823780,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.24961","arxiv_id":"2512.24961","title":"Geometric characterisation of structural and regular equivalences in undirected (hyper)graphs","abstract":"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.","short_abstract":"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 o...","url_abs":"https://arxiv.org/abs/2512.24961","url_pdf":"https://arxiv.org/pdf/2512.24961v1","authors":"[\"Marzieh Eidi\",\"Nina Otter\"]","published":"2025-12-31T16:47:19Z","proceeding":"math.CO","tasks":"[\"math.CO\",\"cs.DM\",\"cs.SI\"]","methods":"[\"LoRA\"]","has_code":false}