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Distances in Higher-Order Networks and the Metric Structure of Hypergraphs

We explore the metric structure of networks with higher-order interactions and introduce a novel definition of distance for hypergraphs that extends the classic methods reported in the literature. The new metric incorporates two critical factors: (1) the inter-node distance within each hyperedge, an...

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Autores principales: Vasilyeva, Ekaterina, Romance, Miguel, Samoylenko, Ivan, Kovalenko, Kirill, Musatov, Daniil, Raigorodskii, Andrey Mihailovich, Boccaletti, Stefano
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10297597/
https://www.ncbi.nlm.nih.gov/pubmed/37372267
http://dx.doi.org/10.3390/e25060923
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author Vasilyeva, Ekaterina
Romance, Miguel
Samoylenko, Ivan
Kovalenko, Kirill
Musatov, Daniil
Raigorodskii, Andrey Mihailovich
Boccaletti, Stefano
author_facet Vasilyeva, Ekaterina
Romance, Miguel
Samoylenko, Ivan
Kovalenko, Kirill
Musatov, Daniil
Raigorodskii, Andrey Mihailovich
Boccaletti, Stefano
author_sort Vasilyeva, Ekaterina
collection PubMed
description We explore the metric structure of networks with higher-order interactions and introduce a novel definition of distance for hypergraphs that extends the classic methods reported in the literature. The new metric incorporates two critical factors: (1) the inter-node distance within each hyperedge, and (2) the distance between hyperedges in the network. As such, it involves the computation of distances in a weighted line graph of the hypergraph. The approach is illustrated with several ad hoc synthetic hypergraphs, where the structural information unveiled by the novel metric is highlighted. Moreover, the method’s performance and effectiveness are shown through computations on large real-world hypergraphs, which indeed reveal new insights into the structural features of networks beyond pairwise interactions. Namely, using the new distance measure, we generalize the definitions of efficiency, closeness and betweenness centrality for the case of hypergraphs. Comparing the values of these generalized measures with their analogs calculated for the hypergraph clique projections, we show that our measures provide significantly different assessments on the characteristics (and roles) of the nodes from the information-transferability point of view. The difference is brighter for hypergraphs in which hyperedges of large sizes are frequent, and nodes relating to these hyperedges are rarely connected by other hyperedges of smaller sizes.
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spelling pubmed-102975972023-06-28 Distances in Higher-Order Networks and the Metric Structure of Hypergraphs Vasilyeva, Ekaterina Romance, Miguel Samoylenko, Ivan Kovalenko, Kirill Musatov, Daniil Raigorodskii, Andrey Mihailovich Boccaletti, Stefano Entropy (Basel) Article We explore the metric structure of networks with higher-order interactions and introduce a novel definition of distance for hypergraphs that extends the classic methods reported in the literature. The new metric incorporates two critical factors: (1) the inter-node distance within each hyperedge, and (2) the distance between hyperedges in the network. As such, it involves the computation of distances in a weighted line graph of the hypergraph. The approach is illustrated with several ad hoc synthetic hypergraphs, where the structural information unveiled by the novel metric is highlighted. Moreover, the method’s performance and effectiveness are shown through computations on large real-world hypergraphs, which indeed reveal new insights into the structural features of networks beyond pairwise interactions. Namely, using the new distance measure, we generalize the definitions of efficiency, closeness and betweenness centrality for the case of hypergraphs. Comparing the values of these generalized measures with their analogs calculated for the hypergraph clique projections, we show that our measures provide significantly different assessments on the characteristics (and roles) of the nodes from the information-transferability point of view. The difference is brighter for hypergraphs in which hyperedges of large sizes are frequent, and nodes relating to these hyperedges are rarely connected by other hyperedges of smaller sizes. MDPI 2023-06-12 /pmc/articles/PMC10297597/ /pubmed/37372267 http://dx.doi.org/10.3390/e25060923 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
Vasilyeva, Ekaterina
Romance, Miguel
Samoylenko, Ivan
Kovalenko, Kirill
Musatov, Daniil
Raigorodskii, Andrey Mihailovich
Boccaletti, Stefano
Distances in Higher-Order Networks and the Metric Structure of Hypergraphs
title Distances in Higher-Order Networks and the Metric Structure of Hypergraphs
title_full Distances in Higher-Order Networks and the Metric Structure of Hypergraphs
title_fullStr Distances in Higher-Order Networks and the Metric Structure of Hypergraphs
title_full_unstemmed Distances in Higher-Order Networks and the Metric Structure of Hypergraphs
title_short Distances in Higher-Order Networks and the Metric Structure of Hypergraphs
title_sort distances in higher-order networks and the metric structure of hypergraphs
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10297597/
https://www.ncbi.nlm.nih.gov/pubmed/37372267
http://dx.doi.org/10.3390/e25060923
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