Entropy bounds for hierarchical molecular networks.

In this paper we derive entropy bounds for hierarchical networks. More precisely, starting from a recently introduced measure to determine the topological entropy of non-hierarchical networks, we provide bounds for estimating the entropy of hierarchical graphs. Apart from bounds to estimate the entr...

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Autores principales:	Matthias Dehmer, Stephan Borgert, Frank Emmert-Streib
Formato:	article
Lenguaje:	EN
Publicado:	Public Library of Science (PLoS) 2008
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/9f3bfced97d34469af22ca1a9d36388d
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spelling	oai:doaj.org-article:9f3bfced97d34469af22ca1a9d36388d2021-11-25T06:18:48ZEntropy bounds for hierarchical molecular networks.1932-620310.1371/journal.pone.0003079https://doaj.org/article/9f3bfced97d34469af22ca1a9d36388d2008-08-01T00:00:00Zhttps://www.ncbi.nlm.nih.gov/pmc/articles/pmid/18769487/pdf/?tool=EBIhttps://doaj.org/toc/1932-6203In this paper we derive entropy bounds for hierarchical networks. More precisely, starting from a recently introduced measure to determine the topological entropy of non-hierarchical networks, we provide bounds for estimating the entropy of hierarchical graphs. Apart from bounds to estimate the entropy of a single hierarchical graph, we see that the derived bounds can also be used for characterizing graph classes. Our contribution is an important extension to previous results about the entropy of non-hierarchical networks because for practical applications hierarchical networks are playing an important role in chemistry and biology. In addition to the derivation of the entropy bounds, we provide a numerical analysis for two special graph classes, rooted trees and generalized trees, and demonstrate hereby not only the computational feasibility of our method but also learn about its characteristics and interpretability with respect to data analysis.Matthias DehmerStephan BorgertFrank Emmert-StreibPublic Library of Science (PLoS)articleMedicineRScienceQENPLoS ONE, Vol 3, Iss 8, p e3079 (2008)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Matthias Dehmer Stephan Borgert Frank Emmert-Streib Entropy bounds for hierarchical molecular networks.
description	In this paper we derive entropy bounds for hierarchical networks. More precisely, starting from a recently introduced measure to determine the topological entropy of non-hierarchical networks, we provide bounds for estimating the entropy of hierarchical graphs. Apart from bounds to estimate the entropy of a single hierarchical graph, we see that the derived bounds can also be used for characterizing graph classes. Our contribution is an important extension to previous results about the entropy of non-hierarchical networks because for practical applications hierarchical networks are playing an important role in chemistry and biology. In addition to the derivation of the entropy bounds, we provide a numerical analysis for two special graph classes, rooted trees and generalized trees, and demonstrate hereby not only the computational feasibility of our method but also learn about its characteristics and interpretability with respect to data analysis.
format	article
author	Matthias Dehmer Stephan Borgert Frank Emmert-Streib
author_facet	Matthias Dehmer Stephan Borgert Frank Emmert-Streib
author_sort	Matthias Dehmer
title	Entropy bounds for hierarchical molecular networks.
title_short	Entropy bounds for hierarchical molecular networks.
title_full	Entropy bounds for hierarchical molecular networks.
title_fullStr	Entropy bounds for hierarchical molecular networks.
title_full_unstemmed	Entropy bounds for hierarchical molecular networks.
title_sort	entropy bounds for hierarchical molecular networks.
publisher	Public Library of Science (PLoS)
publishDate	2008
url	https://doaj.org/article/9f3bfced97d34469af22ca1a9d36388d
work_keys_str_mv	AT matthiasdehmer entropyboundsforhierarchicalmolecularnetworks AT stephanborgert entropyboundsforhierarchicalmolecularnetworks AT frankemmertstreib entropyboundsforhierarchicalmolecularnetworks
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Entropy bounds for hierarchical molecular networks.

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