Connectivity of Random Geometric Hypergraphs

We consider a random geometric hypergraph model based on an underlying bipartite graph. Nodes and hyperedges are sampled uniformly in a domain, and a node is assigned to those hyperedges that lie within a certain radius. From a modelling perspective, we explain how the model captures higher-order co...

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Detalles Bibliográficos
Autores principales: de Kergorlay, Henry-Louis, Higham, Desmond J.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2023
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10670679/
https://www.ncbi.nlm.nih.gov/pubmed/37998246
http://dx.doi.org/10.3390/e25111555
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author de Kergorlay, Henry-Louis
Higham, Desmond J.
author_facet de Kergorlay, Henry-Louis
Higham, Desmond J.
author_sort de Kergorlay, Henry-Louis
collection PubMed
description We consider a random geometric hypergraph model based on an underlying bipartite graph. Nodes and hyperedges are sampled uniformly in a domain, and a node is assigned to those hyperedges that lie within a certain radius. From a modelling perspective, we explain how the model captures higher-order connections that arise in real data sets. Our main contribution is to study the connectivity properties of the model. In an asymptotic limit where the number of nodes and hyperedges grow in tandem, we give a condition on the radius that guarantees connectivity.
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spelling pubmed-106706792023-11-17 Connectivity of Random Geometric Hypergraphs de Kergorlay, Henry-Louis Higham, Desmond J. Entropy (Basel) Article We consider a random geometric hypergraph model based on an underlying bipartite graph. Nodes and hyperedges are sampled uniformly in a domain, and a node is assigned to those hyperedges that lie within a certain radius. From a modelling perspective, we explain how the model captures higher-order connections that arise in real data sets. Our main contribution is to study the connectivity properties of the model. In an asymptotic limit where the number of nodes and hyperedges grow in tandem, we give a condition on the radius that guarantees connectivity. MDPI 2023-11-17 /pmc/articles/PMC10670679/ /pubmed/37998246 http://dx.doi.org/10.3390/e25111555 Text en © 2023 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
de Kergorlay, Henry-Louis
Higham, Desmond J.
Connectivity of Random Geometric Hypergraphs
title Connectivity of Random Geometric Hypergraphs
title_full Connectivity of Random Geometric Hypergraphs
title_fullStr Connectivity of Random Geometric Hypergraphs
title_full_unstemmed Connectivity of Random Geometric Hypergraphs
title_short Connectivity of Random Geometric Hypergraphs
title_sort connectivity of random geometric hypergraphs
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10670679/
https://www.ncbi.nlm.nih.gov/pubmed/37998246
http://dx.doi.org/10.3390/e25111555
work_keys_str_mv AT dekergorlayhenrylouis connectivityofrandomgeometrichypergraphs
AT highamdesmondj connectivityofrandomgeometrichypergraphs

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