Eigenvalue-based entropy in directed complex networks.

Entropy is an important index for describing the structure, function, and evolution of network. The existing research on entropy is primarily applied to undirected networks. Compared with an undirected network, a directed network involves a special asymmetric transfer. The research on the entropy of...

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Autores principales:	Yan Sun, Haixing Zhao, Jing Liang, Xiujuan Ma
Formato:	article
Lenguaje:	EN
Publicado:	Public Library of Science (PLoS) 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/b6c929e7554342e682f55ef6c564576e
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id	oai:doaj.org-article:b6c929e7554342e682f55ef6c564576e
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spelling	oai:doaj.org-article:b6c929e7554342e682f55ef6c564576e2021-12-02T20:03:51ZEigenvalue-based entropy in directed complex networks.1932-620310.1371/journal.pone.0251993https://doaj.org/article/b6c929e7554342e682f55ef6c564576e2021-01-01T00:00:00Zhttps://doi.org/10.1371/journal.pone.0251993https://doaj.org/toc/1932-6203Entropy is an important index for describing the structure, function, and evolution of network. The existing research on entropy is primarily applied to undirected networks. Compared with an undirected network, a directed network involves a special asymmetric transfer. The research on the entropy of directed networks is very significant to effectively quantify the structural information of the whole network. Typical complex network models include nearest-neighbour coupling network, small-world network, scale-free network, and random network. These network models are abstracted as undirected graphs without considering the direction of node connection. For complex networks, modeling through the direction of network nodes is extremely challenging. In this paper, based on these typical models of complex network, a directed network model considering node connection in-direction is proposed, and the eigenvalue entropies of three matrices in the directed network is defined and studied, where the three matrices are adjacency matrix, in-degree Laplacian matrix and in-degree signless Laplacian matrix. The eigenvalue-based entropies of three matrices are calculated in directed nearest-neighbor coupling, directed small world, directed scale-free and directed random networks. Through the simulation experiment on the real directed network, the result shows that the eigenvalue entropy of the real directed network is between the eigenvalue entropy of directed scale-free network and directed small-world network.Yan SunHaixing ZhaoJing LiangXiujuan MaPublic Library of Science (PLoS)articleMedicineRScienceQENPLoS ONE, Vol 16, Iss 6, p e0251993 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Yan Sun Haixing Zhao Jing Liang Xiujuan Ma Eigenvalue-based entropy in directed complex networks.
description	Entropy is an important index for describing the structure, function, and evolution of network. The existing research on entropy is primarily applied to undirected networks. Compared with an undirected network, a directed network involves a special asymmetric transfer. The research on the entropy of directed networks is very significant to effectively quantify the structural information of the whole network. Typical complex network models include nearest-neighbour coupling network, small-world network, scale-free network, and random network. These network models are abstracted as undirected graphs without considering the direction of node connection. For complex networks, modeling through the direction of network nodes is extremely challenging. In this paper, based on these typical models of complex network, a directed network model considering node connection in-direction is proposed, and the eigenvalue entropies of three matrices in the directed network is defined and studied, where the three matrices are adjacency matrix, in-degree Laplacian matrix and in-degree signless Laplacian matrix. The eigenvalue-based entropies of three matrices are calculated in directed nearest-neighbor coupling, directed small world, directed scale-free and directed random networks. Through the simulation experiment on the real directed network, the result shows that the eigenvalue entropy of the real directed network is between the eigenvalue entropy of directed scale-free network and directed small-world network.
format	article
author	Yan Sun Haixing Zhao Jing Liang Xiujuan Ma
author_facet	Yan Sun Haixing Zhao Jing Liang Xiujuan Ma
author_sort	Yan Sun
title	Eigenvalue-based entropy in directed complex networks.
title_short	Eigenvalue-based entropy in directed complex networks.
title_full	Eigenvalue-based entropy in directed complex networks.
title_fullStr	Eigenvalue-based entropy in directed complex networks.
title_full_unstemmed	Eigenvalue-based entropy in directed complex networks.
title_sort	eigenvalue-based entropy in directed complex networks.
publisher	Public Library of Science (PLoS)
publishDate	2021
url	https://doaj.org/article/b6c929e7554342e682f55ef6c564576e
work_keys_str_mv	AT yansun eigenvaluebasedentropyindirectedcomplexnetworks AT haixingzhao eigenvaluebasedentropyindirectedcomplexnetworks AT jingliang eigenvaluebasedentropyindirectedcomplexnetworks AT xiujuanma eigenvaluebasedentropyindirectedcomplexnetworks
_version_	1718375624890908672

Eigenvalue-based entropy in directed complex networks.

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