Hierarchical coefficient of a multifractal based network
Autor(a) principal: | |
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Data de Publicação: | 2014 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFRN |
Texto Completo: | https://repositorio.ufrn.br/handle/123456789/30640 |
Resumo: | The hierarchical property for a general class of networks stands for a power-law relation between clustering coefficient, CC and connectivity k: CC ∝ kβ. This relation is empirically verified in several biologic and social networks, as well as in random and deterministic network models, in special for hierarchical networks. In this work we show that the hierarchical property is also present in a Lucena network. To create a Lucena network we use the dual of a multifractal lattice ML, the vertices are the sites of the ML and links are established between neighbouring lattices, therefore this network is space filling and planar. Besides a Lucena network shows a scale-free distribution of connectivity. We deduce a relation for the maximal local clustering coefficient CCmaxiof a vertex i in a planar graph. This condition expresses that the number of links among neighbour, N△, of a vertexi is equal to its connectivity ki, that means: N△ = ki. The Lucena network fulfils the condition N△ ≃ ki independent of ki and the anisotropy of ML. In addition, CCmax implies the threshold β = 1 for the hierarchical property for any scale-free planar network |
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Moreira, Darlan AraújoLucena, Liacir dos SantosCorso, Gilberto2020-11-23T20:45:34Z2020-11-23T20:45:34Z2014-02-15MOREIRA, Darlan A.; LUCENA, Liacir dos Santos; CORSO, Gilberto. Hierarchical coefficient of a multifractal based network. Physica A: Statistical Mechanics and its Applications, [S.L.], v. 396, p. 242-247, fev. 2014. Disponível em: https://www.sciencedirect.com/science/article/abs/pii/S0378437113010625?via%3Dihub. Acesso em: 08 set. 2020. http://dx.doi.org/10.1016/j.physa.2013.11.020.0378-437110.1016/j.physa.2013.11.020.https://repositorio.ufrn.br/handle/123456789/30640ElsevierAttribution 3.0 Brazilhttp://creativecommons.org/licenses/by/3.0/br/info:eu-repo/semantics/openAccessMultifractal latticeHierarchical networkPlanar graphApollonius networkSpace filling networkHierarchical coefficient of a multifractal based networkinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleThe hierarchical property for a general class of networks stands for a power-law relation between clustering coefficient, CC and connectivity k: CC ∝ kβ. This relation is empirically verified in several biologic and social networks, as well as in random and deterministic network models, in special for hierarchical networks. In this work we show that the hierarchical property is also present in a Lucena network. To create a Lucena network we use the dual of a multifractal lattice ML, the vertices are the sites of the ML and links are established between neighbouring lattices, therefore this network is space filling and planar. Besides a Lucena network shows a scale-free distribution of connectivity. We deduce a relation for the maximal local clustering coefficient CCmaxiof a vertex i in a planar graph. This condition expresses that the number of links among neighbour, N△, of a vertexi is equal to its connectivity ki, that means: N△ = ki. The Lucena network fulfils the condition N△ ≃ ki independent of ki and the anisotropy of ML. In addition, CCmax implies the threshold β = 1 for the hierarchical property for any scale-free planar networkengreponame:Repositório Institucional da UFRNinstname:Universidade Federal do Rio Grande do Norte (UFRN)instacron:UFRNORIGINALHierarchicalCoefficientMultifractal_Moreira_2014.pdfHierarchicalCoefficientMultifractal_Moreira_2014.pdfapplication/pdf501945https://repositorio.ufrn.br/bitstream/123456789/30640/1/HierarchicalCoefficientMultifractal_Moreira_2014.pdf7c0a96f4cb55de460cb4bd81797cccebMD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8914https://repositorio.ufrn.br/bitstream/123456789/30640/2/license_rdf4d2950bda3d176f570a9f8b328dfbbefMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81484https://repositorio.ufrn.br/bitstream/123456789/30640/3/license.txte9597aa2854d128fd968be5edc8a28d9MD53TEXTHierarchicalCoefficientMultifractal_MOREIRA_2014.pdf.txtHierarchicalCoefficientMultifractal_MOREIRA_2014.pdf.txtExtracted texttext/plain22053https://repositorio.ufrn.br/bitstream/123456789/30640/4/HierarchicalCoefficientMultifractal_MOREIRA_2014.pdf.txt22ed3c42390d7e646c946d845bee02cbMD54THUMBNAILHierarchicalCoefficientMultifractal_MOREIRA_2014.pdf.jpgHierarchicalCoefficientMultifractal_MOREIRA_2014.pdf.jpgGenerated Thumbnailimage/jpeg1745https://repositorio.ufrn.br/bitstream/123456789/30640/5/HierarchicalCoefficientMultifractal_MOREIRA_2014.pdf.jpgc618906a40d860658dfe675e87956b65MD55123456789/306402021-11-10 16:41:34.308oai:https://repositorio.ufrn.br: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Repositório de PublicaçõesPUBhttp://repositorio.ufrn.br/oai/opendoar:2021-11-10T19:41:34Repositório Institucional da UFRN - Universidade Federal do Rio Grande do Norte (UFRN)false |
dc.title.pt_BR.fl_str_mv |
Hierarchical coefficient of a multifractal based network |
title |
Hierarchical coefficient of a multifractal based network |
spellingShingle |
Hierarchical coefficient of a multifractal based network Moreira, Darlan Araújo Multifractal lattice Hierarchical network Planar graph Apollonius network Space filling network |
title_short |
Hierarchical coefficient of a multifractal based network |
title_full |
Hierarchical coefficient of a multifractal based network |
title_fullStr |
Hierarchical coefficient of a multifractal based network |
title_full_unstemmed |
Hierarchical coefficient of a multifractal based network |
title_sort |
Hierarchical coefficient of a multifractal based network |
author |
Moreira, Darlan Araújo |
author_facet |
Moreira, Darlan Araújo Lucena, Liacir dos Santos Corso, Gilberto |
author_role |
author |
author2 |
Lucena, Liacir dos Santos Corso, Gilberto |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Moreira, Darlan Araújo Lucena, Liacir dos Santos Corso, Gilberto |
dc.subject.por.fl_str_mv |
Multifractal lattice Hierarchical network Planar graph Apollonius network Space filling network |
topic |
Multifractal lattice Hierarchical network Planar graph Apollonius network Space filling network |
description |
The hierarchical property for a general class of networks stands for a power-law relation between clustering coefficient, CC and connectivity k: CC ∝ kβ. This relation is empirically verified in several biologic and social networks, as well as in random and deterministic network models, in special for hierarchical networks. In this work we show that the hierarchical property is also present in a Lucena network. To create a Lucena network we use the dual of a multifractal lattice ML, the vertices are the sites of the ML and links are established between neighbouring lattices, therefore this network is space filling and planar. Besides a Lucena network shows a scale-free distribution of connectivity. We deduce a relation for the maximal local clustering coefficient CCmaxiof a vertex i in a planar graph. This condition expresses that the number of links among neighbour, N△, of a vertexi is equal to its connectivity ki, that means: N△ = ki. The Lucena network fulfils the condition N△ ≃ ki independent of ki and the anisotropy of ML. In addition, CCmax implies the threshold β = 1 for the hierarchical property for any scale-free planar network |
publishDate |
2014 |
dc.date.issued.fl_str_mv |
2014-02-15 |
dc.date.accessioned.fl_str_mv |
2020-11-23T20:45:34Z |
dc.date.available.fl_str_mv |
2020-11-23T20:45:34Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
MOREIRA, Darlan A.; LUCENA, Liacir dos Santos; CORSO, Gilberto. Hierarchical coefficient of a multifractal based network. Physica A: Statistical Mechanics and its Applications, [S.L.], v. 396, p. 242-247, fev. 2014. Disponível em: https://www.sciencedirect.com/science/article/abs/pii/S0378437113010625?via%3Dihub. Acesso em: 08 set. 2020. http://dx.doi.org/10.1016/j.physa.2013.11.020. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufrn.br/handle/123456789/30640 |
dc.identifier.issn.none.fl_str_mv |
0378-4371 10.1016/j.physa.2013.11.020. |
identifier_str_mv |
MOREIRA, Darlan A.; LUCENA, Liacir dos Santos; CORSO, Gilberto. Hierarchical coefficient of a multifractal based network. Physica A: Statistical Mechanics and its Applications, [S.L.], v. 396, p. 242-247, fev. 2014. Disponível em: https://www.sciencedirect.com/science/article/abs/pii/S0378437113010625?via%3Dihub. Acesso em: 08 set. 2020. http://dx.doi.org/10.1016/j.physa.2013.11.020. 0378-4371 10.1016/j.physa.2013.11.020. |
url |
https://repositorio.ufrn.br/handle/123456789/30640 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
Attribution 3.0 Brazil http://creativecommons.org/licenses/by/3.0/br/ info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Attribution 3.0 Brazil http://creativecommons.org/licenses/by/3.0/br/ |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Elsevier |
publisher.none.fl_str_mv |
Elsevier |
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reponame:Repositório Institucional da UFRN instname:Universidade Federal do Rio Grande do Norte (UFRN) instacron:UFRN |
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Universidade Federal do Rio Grande do Norte (UFRN) |
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UFRN |
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UFRN |
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Repositório Institucional da UFRN |
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Repositório Institucional da UFRN |
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