Asymptotic entropy of the Gibbs state of complex networks

In this work we study the entropy of the Gibbs state corresponding to a graph. The Gibbs state is obtained from the Laplacian, normalized Laplacian or adjacency matrices associated with a graph. We calculated the entropy of the Gibbs state for a few classes of graphs and studied their behavior with...

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Autores principales: Glos, Adam, Krawiec, Aleksandra, Pawela, Łukasz
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group UK 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7801599/
https://www.ncbi.nlm.nih.gov/pubmed/33431960
http://dx.doi.org/10.1038/s41598-020-78626-2
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author Glos, Adam
Krawiec, Aleksandra
Pawela, Łukasz
author_facet Glos, Adam
Krawiec, Aleksandra
Pawela, Łukasz
author_sort Glos, Adam
collection PubMed
description In this work we study the entropy of the Gibbs state corresponding to a graph. The Gibbs state is obtained from the Laplacian, normalized Laplacian or adjacency matrices associated with a graph. We calculated the entropy of the Gibbs state for a few classes of graphs and studied their behavior with changing graph order and temperature. We illustrate our analytical results with numerical simulations for Erdős–Rényi, Watts–Strogatz, Barabási–Albert and Chung–Lu graph models and a few real-world graphs. Our results show that the behavior of Gibbs entropy as a function of the temperature differs for a choice of real networks when compared to the random Erdős–Rényi graphs.
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spelling pubmed-78015992021-01-12 Asymptotic entropy of the Gibbs state of complex networks Glos, Adam Krawiec, Aleksandra Pawela, Łukasz Sci Rep Article In this work we study the entropy of the Gibbs state corresponding to a graph. The Gibbs state is obtained from the Laplacian, normalized Laplacian or adjacency matrices associated with a graph. We calculated the entropy of the Gibbs state for a few classes of graphs and studied their behavior with changing graph order and temperature. We illustrate our analytical results with numerical simulations for Erdős–Rényi, Watts–Strogatz, Barabási–Albert and Chung–Lu graph models and a few real-world graphs. Our results show that the behavior of Gibbs entropy as a function of the temperature differs for a choice of real networks when compared to the random Erdős–Rényi graphs. Nature Publishing Group UK 2021-01-11 /pmc/articles/PMC7801599/ /pubmed/33431960 http://dx.doi.org/10.1038/s41598-020-78626-2 Text en © The Author(s) 2021 Open AccessThis 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 licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence 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 licence, visit http://creativecommons.org/licenses/by/4.0/.
spellingShingle Article
Glos, Adam
Krawiec, Aleksandra
Pawela, Łukasz
Asymptotic entropy of the Gibbs state of complex networks
title Asymptotic entropy of the Gibbs state of complex networks
title_full Asymptotic entropy of the Gibbs state of complex networks
title_fullStr Asymptotic entropy of the Gibbs state of complex networks
title_full_unstemmed Asymptotic entropy of the Gibbs state of complex networks
title_short Asymptotic entropy of the Gibbs state of complex networks
title_sort asymptotic entropy of the gibbs state of complex networks
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7801599/
https://www.ncbi.nlm.nih.gov/pubmed/33431960
http://dx.doi.org/10.1038/s41598-020-78626-2
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