Graph hierarchy: a novel framework to analyse hierarchical structures in complex networks

Abstract Trophic coherence, a measure of a graph’s hierarchical organisation, has been shown to be linked to a graph’s structural and dynamical aspects such as cyclicity, stability and normality. Trophic levels of vertices can reveal their functional properties, partition and rank the vertices accor...

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Autores principales:	Giannis Moutsinas, Choudhry Shuaib, Weisi Guo, Stephen Jarvis
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/f057a85876a74abc9e7182332521383b
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id	oai:doaj.org-article:f057a85876a74abc9e7182332521383b
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spelling	oai:doaj.org-article:f057a85876a74abc9e7182332521383b2021-12-02T15:39:41ZGraph hierarchy: a novel framework to analyse hierarchical structures in complex networks10.1038/s41598-021-93161-42045-2322https://doaj.org/article/f057a85876a74abc9e7182332521383b2021-07-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-93161-4https://doaj.org/toc/2045-2322Abstract Trophic coherence, a measure of a graph’s hierarchical organisation, has been shown to be linked to a graph’s structural and dynamical aspects such as cyclicity, stability and normality. Trophic levels of vertices can reveal their functional properties, partition and rank the vertices accordingly. Trophic levels and hence trophic coherence can only be defined on graphs with basal vertices, i.e. vertices with zero in-degree. Consequently, trophic analysis of graphs had been restricted until now. In this paper we introduce a hierarchical framework which can be defined on any simple graph. Within this general framework, we develop several metrics: hierarchical levels, a generalisation of the notion of trophic levels, influence centrality, a measure of a vertex’s ability to influence dynamics, and democracy coefficient, a measure of overall feedback in the system. We discuss how our generalisation relates to previous attempts and what new insights are illuminated on the topological and dynamical aspects of graphs. Finally, we show how the hierarchical structure of a network relates to the incidence rate in a SIS epidemic model and the economic insights we can gain through it.Giannis MoutsinasChoudhry ShuaibWeisi GuoStephen JarvisNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-11 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Giannis Moutsinas Choudhry Shuaib Weisi Guo Stephen Jarvis Graph hierarchy: a novel framework to analyse hierarchical structures in complex networks
description	Abstract Trophic coherence, a measure of a graph’s hierarchical organisation, has been shown to be linked to a graph’s structural and dynamical aspects such as cyclicity, stability and normality. Trophic levels of vertices can reveal their functional properties, partition and rank the vertices accordingly. Trophic levels and hence trophic coherence can only be defined on graphs with basal vertices, i.e. vertices with zero in-degree. Consequently, trophic analysis of graphs had been restricted until now. In this paper we introduce a hierarchical framework which can be defined on any simple graph. Within this general framework, we develop several metrics: hierarchical levels, a generalisation of the notion of trophic levels, influence centrality, a measure of a vertex’s ability to influence dynamics, and democracy coefficient, a measure of overall feedback in the system. We discuss how our generalisation relates to previous attempts and what new insights are illuminated on the topological and dynamical aspects of graphs. Finally, we show how the hierarchical structure of a network relates to the incidence rate in a SIS epidemic model and the economic insights we can gain through it.
format	article
author	Giannis Moutsinas Choudhry Shuaib Weisi Guo Stephen Jarvis
author_facet	Giannis Moutsinas Choudhry Shuaib Weisi Guo Stephen Jarvis
author_sort	Giannis Moutsinas
title	Graph hierarchy: a novel framework to analyse hierarchical structures in complex networks
title_short	Graph hierarchy: a novel framework to analyse hierarchical structures in complex networks
title_full	Graph hierarchy: a novel framework to analyse hierarchical structures in complex networks
title_fullStr	Graph hierarchy: a novel framework to analyse hierarchical structures in complex networks
title_full_unstemmed	Graph hierarchy: a novel framework to analyse hierarchical structures in complex networks
title_sort	graph hierarchy: a novel framework to analyse hierarchical structures in complex networks
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/f057a85876a74abc9e7182332521383b
work_keys_str_mv	AT giannismoutsinas graphhierarchyanovelframeworktoanalysehierarchicalstructuresincomplexnetworks AT choudhryshuaib graphhierarchyanovelframeworktoanalysehierarchicalstructuresincomplexnetworks AT weisiguo graphhierarchyanovelframeworktoanalysehierarchicalstructuresincomplexnetworks AT stephenjarvis graphhierarchyanovelframeworktoanalysehierarchicalstructuresincomplexnetworks
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Graph hierarchy: a novel framework to analyse hierarchical structures in complex networks

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