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Generalised thresholding of hidden variable network models with scale-free property
The hidden variable formalism (based on the assumption of some intrinsic node parameters) turned out to be a remarkably efficient and powerful approach in describing and analyzing the topology of complex networks. Owing to one of its most advantageous property - namely proven to be able to reproduce...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Nature Publishing Group UK
2019
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6677767/ https://www.ncbi.nlm.nih.gov/pubmed/31375716 http://dx.doi.org/10.1038/s41598-019-47628-0 |
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author | Balogh, Sámuel G. Pollner, Péter Palla, Gergely |
author_facet | Balogh, Sámuel G. Pollner, Péter Palla, Gergely |
author_sort | Balogh, Sámuel G. |
collection | PubMed |
description | The hidden variable formalism (based on the assumption of some intrinsic node parameters) turned out to be a remarkably efficient and powerful approach in describing and analyzing the topology of complex networks. Owing to one of its most advantageous property - namely proven to be able to reproduce a wide range of different degree distribution forms - it has become a standard tool for generating networks having the scale-free property. One of the most intensively studied version of this model is based on a thresholding mechanism of the exponentially distributed hidden variables associated to the nodes (intrinsic vertex weights), which give rise to the emergence of a scale-free network where the degree distribution p(k) ~ k(−γ) is decaying with an exponent of γ = 2. Here we propose a generalization and modification of this model by extending the set of connection probabilities and hidden variable distributions that lead to the aforementioned degree distribution, and analyze the conditions leading to the above behavior analytically. In addition, we propose a relaxation of the hard threshold in the connection probabilities, which opens up the possibility for obtaining sparse scale free networks with arbitrary scaling exponent. |
format | Online Article Text |
id | pubmed-6677767 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2019 |
publisher | Nature Publishing Group UK |
record_format | MEDLINE/PubMed |
spelling | pubmed-66777672019-08-08 Generalised thresholding of hidden variable network models with scale-free property Balogh, Sámuel G. Pollner, Péter Palla, Gergely Sci Rep Article The hidden variable formalism (based on the assumption of some intrinsic node parameters) turned out to be a remarkably efficient and powerful approach in describing and analyzing the topology of complex networks. Owing to one of its most advantageous property - namely proven to be able to reproduce a wide range of different degree distribution forms - it has become a standard tool for generating networks having the scale-free property. One of the most intensively studied version of this model is based on a thresholding mechanism of the exponentially distributed hidden variables associated to the nodes (intrinsic vertex weights), which give rise to the emergence of a scale-free network where the degree distribution p(k) ~ k(−γ) is decaying with an exponent of γ = 2. Here we propose a generalization and modification of this model by extending the set of connection probabilities and hidden variable distributions that lead to the aforementioned degree distribution, and analyze the conditions leading to the above behavior analytically. In addition, we propose a relaxation of the hard threshold in the connection probabilities, which opens up the possibility for obtaining sparse scale free networks with arbitrary scaling exponent. Nature Publishing Group UK 2019-08-02 /pmc/articles/PMC6677767/ /pubmed/31375716 http://dx.doi.org/10.1038/s41598-019-47628-0 Text en © The Author(s) 2019 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. |
spellingShingle | Article Balogh, Sámuel G. Pollner, Péter Palla, Gergely Generalised thresholding of hidden variable network models with scale-free property |
title | Generalised thresholding of hidden variable network models with scale-free property |
title_full | Generalised thresholding of hidden variable network models with scale-free property |
title_fullStr | Generalised thresholding of hidden variable network models with scale-free property |
title_full_unstemmed | Generalised thresholding of hidden variable network models with scale-free property |
title_short | Generalised thresholding of hidden variable network models with scale-free property |
title_sort | generalised thresholding of hidden variable network models with scale-free property |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6677767/ https://www.ncbi.nlm.nih.gov/pubmed/31375716 http://dx.doi.org/10.1038/s41598-019-47628-0 |
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