Google matrix

Autores
Ermann, Leonardo; Frahm, Klaus; Shepelyansky, Dima
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The Google matrix G of a directed network is a stochastic square matrix with nonnegative matrix elements and the sum of elements in each column being equal to unity. This matrix describes a Markov chain (Markov, 1906-a) of transitions of a random surfer performing jumps on a network of nodes connected by directed links. The network is characterized by an adjacency matrix Aij with elements Aij=1 if node j points to node i and zero otherwise. The matrix of Markov transitions Sij is constructed from the adjacency matrix Aij by normalization of the sum of column elements to unity and replacing columns with only zero elements (dangling nodes) with equal elements 1/N where N is the matrix size (number of nodes). Then the elements of the Google matrix are defined as Gij=αSij+(1−α)/N.
Fil: Ermann, Leonardo. Comisión Nacional de Energía Atómica. Centro Atómico Constituyentes. Gerencia de Investigación y Aplicaciones; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Frahm, Klaus. Universitá Paul Sabatier; Francia
Fil: Shepelyansky, Dima. Universitá Paul Sabatier; Francia
Materia
COMPLEX NETWORKS
SPECTRUM
QUANTUM CHAOS
COMPLEX SYSTEMS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/18029
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/18029
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Google matrixErmann, LeonardoFrahm, KlausShepelyansky, DimaCOMPLEX NETWORKSSPECTRUMQUANTUM CHAOSCOMPLEX SYSTEMShttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1The Google matrix G of a directed network is a stochastic square matrix with nonnegative matrix elements and the sum of elements in each column being equal to unity. This matrix describes a Markov chain (Markov, 1906-a) of transitions of a random surfer performing jumps on a network of nodes connected by directed links. The network is characterized by an adjacency matrix Aij with elements Aij=1 if node j points to node i and zero otherwise. The matrix of Markov transitions Sij is constructed from the adjacency matrix Aij by normalization of the sum of column elements to unity and replacing columns with only zero elements (dangling nodes) with equal elements 1/N where N is the matrix size (number of nodes). Then the elements of the Google matrix are defined as Gij=αSij+(1−α)/N.Fil: Ermann, Leonardo. Comisión Nacional de Energía Atómica. Centro Atómico Constituyentes. Gerencia de Investigación y Aplicaciones; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Frahm, Klaus. Universitá Paul Sabatier; FranciaFil: Shepelyansky, Dima. Universitá Paul Sabatier; FranciaScholarpedia2016-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/18029Ermann, Leonardo; Frahm, Klaus; Shepelyansky, Dima; Google matrix; Scholarpedia; Scholarpedia; 11; 11; 11-20161941-6016enginfo:eu-repo/semantics/altIdentifier/url/http://www.scholarpedia.org/article/Google_matrixinfo:eu-repo/semantics/altIdentifier/doi/10.4249/scholarpedia.30944info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:57:07Zoai:ri.conicet.gov.ar:11336/18029instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:57:07.54CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Google matrix
title Google matrix
spellingShingle Google matrix
Ermann, Leonardo
COMPLEX NETWORKS
SPECTRUM
QUANTUM CHAOS
COMPLEX SYSTEMS
title_short Google matrix
title_full Google matrix
title_fullStr Google matrix
title_full_unstemmed Google matrix
title_sort Google matrix
dc.creator.none.fl_str_mv Ermann, Leonardo
Frahm, Klaus
Shepelyansky, Dima
author Ermann, Leonardo
author_facet Ermann, Leonardo
Frahm, Klaus
Shepelyansky, Dima
author_role author
author2 Frahm, Klaus
Shepelyansky, Dima
author2_role author
author
dc.subject.none.fl_str_mv COMPLEX NETWORKS
SPECTRUM
QUANTUM CHAOS
COMPLEX SYSTEMS
topic COMPLEX NETWORKS
SPECTRUM
QUANTUM CHAOS
COMPLEX SYSTEMS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The Google matrix G of a directed network is a stochastic square matrix with nonnegative matrix elements and the sum of elements in each column being equal to unity. This matrix describes a Markov chain (Markov, 1906-a) of transitions of a random surfer performing jumps on a network of nodes connected by directed links. The network is characterized by an adjacency matrix Aij with elements Aij=1 if node j points to node i and zero otherwise. The matrix of Markov transitions Sij is constructed from the adjacency matrix Aij by normalization of the sum of column elements to unity and replacing columns with only zero elements (dangling nodes) with equal elements 1/N where N is the matrix size (number of nodes). Then the elements of the Google matrix are defined as Gij=αSij+(1−α)/N.
Fil: Ermann, Leonardo. Comisión Nacional de Energía Atómica. Centro Atómico Constituyentes. Gerencia de Investigación y Aplicaciones; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Frahm, Klaus. Universitá Paul Sabatier; Francia
Fil: Shepelyansky, Dima. Universitá Paul Sabatier; Francia
description The Google matrix G of a directed network is a stochastic square matrix with nonnegative matrix elements and the sum of elements in each column being equal to unity. This matrix describes a Markov chain (Markov, 1906-a) of transitions of a random surfer performing jumps on a network of nodes connected by directed links. The network is characterized by an adjacency matrix Aij with elements Aij=1 if node j points to node i and zero otherwise. The matrix of Markov transitions Sij is constructed from the adjacency matrix Aij by normalization of the sum of column elements to unity and replacing columns with only zero elements (dangling nodes) with equal elements 1/N where N is the matrix size (number of nodes). Then the elements of the Google matrix are defined as Gij=αSij+(1−α)/N.
publishDate 2016
dc.date.none.fl_str_mv 2016-11
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/18029
Ermann, Leonardo; Frahm, Klaus; Shepelyansky, Dima; Google matrix; Scholarpedia; Scholarpedia; 11; 11; 11-2016
1941-6016
url http://hdl.handle.net/11336/18029
identifier_str_mv Ermann, Leonardo; Frahm, Klaus; Shepelyansky, Dima; Google matrix; Scholarpedia; Scholarpedia; 11; 11; 11-2016
1941-6016
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.scholarpedia.org/article/Google_matrix
info:eu-repo/semantics/altIdentifier/doi/10.4249/scholarpedia.30944
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Scholarpedia
publisher.none.fl_str_mv Scholarpedia
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1842269440913178624
score 13.13397

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