Optimisation of the coalescent hyperbolic embedding of complex networks

Abstract Several observations indicate the existence of a latent hyperbolic space behind real networks that makes their structure very intuitive in the sense that the probability for a connection is decreasing with the hyperbolic distance between the nodes. A remarkable network model generating rand...

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Autores principales:	Bianka Kovács, Gergely Palla
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/a35da2b485134c2e87f02213d515af79
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spelling	oai:doaj.org-article:a35da2b485134c2e87f02213d515af792021-12-02T14:26:20ZOptimisation of the coalescent hyperbolic embedding of complex networks10.1038/s41598-021-87333-52045-2322https://doaj.org/article/a35da2b485134c2e87f02213d515af792021-04-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-87333-5https://doaj.org/toc/2045-2322Abstract Several observations indicate the existence of a latent hyperbolic space behind real networks that makes their structure very intuitive in the sense that the probability for a connection is decreasing with the hyperbolic distance between the nodes. A remarkable network model generating random graphs along this line is the popularity-similarity optimisation (PSO) model, offering a scale-free degree distribution, high clustering and the small-world property at the same time. These results provide a strong motivation for the development of hyperbolic embedding algorithms, that tackle the problem of finding the optimal hyperbolic coordinates of the nodes based on the network structure. A very promising recent approach for hyperbolic embedding is provided by the noncentered minimum curvilinear embedding (ncMCE) method, belonging to the family of coalescent embedding algorithms. This approach offers a high-quality embedding at a low running time. In the present work we propose a further optimisation of the angular coordinates in this framework that seems to reduce the logarithmic loss and increase the greedy routing score of the embedding compared to the original version, thereby adding an extra improvement to the quality of the inferred hyperbolic coordinates.Bianka KovácsGergely PallaNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-15 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Bianka Kovács Gergely Palla Optimisation of the coalescent hyperbolic embedding of complex networks
description	Abstract Several observations indicate the existence of a latent hyperbolic space behind real networks that makes their structure very intuitive in the sense that the probability for a connection is decreasing with the hyperbolic distance between the nodes. A remarkable network model generating random graphs along this line is the popularity-similarity optimisation (PSO) model, offering a scale-free degree distribution, high clustering and the small-world property at the same time. These results provide a strong motivation for the development of hyperbolic embedding algorithms, that tackle the problem of finding the optimal hyperbolic coordinates of the nodes based on the network structure. A very promising recent approach for hyperbolic embedding is provided by the noncentered minimum curvilinear embedding (ncMCE) method, belonging to the family of coalescent embedding algorithms. This approach offers a high-quality embedding at a low running time. In the present work we propose a further optimisation of the angular coordinates in this framework that seems to reduce the logarithmic loss and increase the greedy routing score of the embedding compared to the original version, thereby adding an extra improvement to the quality of the inferred hyperbolic coordinates.
format	article
author	Bianka Kovács Gergely Palla
author_facet	Bianka Kovács Gergely Palla
author_sort	Bianka Kovács
title	Optimisation of the coalescent hyperbolic embedding of complex networks
title_short	Optimisation of the coalescent hyperbolic embedding of complex networks
title_full	Optimisation of the coalescent hyperbolic embedding of complex networks
title_fullStr	Optimisation of the coalescent hyperbolic embedding of complex networks
title_full_unstemmed	Optimisation of the coalescent hyperbolic embedding of complex networks
title_sort	optimisation of the coalescent hyperbolic embedding of complex networks
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/a35da2b485134c2e87f02213d515af79
work_keys_str_mv	AT biankakovacs optimisationofthecoalescenthyperbolicembeddingofcomplexnetworks AT gergelypalla optimisationofthecoalescenthyperbolicembeddingofcomplexnetworks
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Optimisation of the coalescent hyperbolic embedding of complex networks

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