Spectral partitioning of random graphs with given expected degrees

Autores
Goerdt, Andreas; Coja-Oghlan, Amin; Lanka, André
Año de publicación
2006
Idioma
inglés
Tipo de recurso
documento de conferencia
Estado
versión publicada
Descripción
It is a well established fact, that - in the case of classical random graphs like (variants of) Gn,p or random regular graphs - spectral methods yield efficient algorithms for clustering (e. g. colouring or bisection) problems. The theory of large networks emerging recently provides convincing evidence that such networks, albeit looking random in some sense, cannot sensibly be described by classical random graphs. A variety of new types of random graphs have been introduced. One of these types is characterized by the fact that we have a fixed expected degree sequence, that is for each vertex its expected degree is given. Recent theoretical work confirms that spectral methods can be successfully applied to clustering problems for such random graphs, too - provided that the expected degrees are not too small, in fact ≥ log6 n. In this case however the degree of each vertex is concentrated about its expectation. We show how to remove this restriction and apply spectral methods when the expected degrees are bounded below just by a suitable constant. Our results rely on the observation that techniques developed for the classical sparse Gn,p random graph (that is p = c/n) can be transferred to the present situation, when we consider a suitably normalized adjacency matrix: We divide each entry of the adjacency matrix by the product of the expected degrees of the incident vertices. Given the host of spectral techniques developed for Gn,p this observation should be of independent interest.
4th IFIP International Conference on Theoretical Computer Science
Red de Universidades con Carreras en Informática (RedUNCI)
Materia
Ciencias Informáticas
random graph
spectral techniques
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/24421

id SEDICI_42a828b92086c3441a64094bc275b96d
oai_identifier_str oai:sedici.unlp.edu.ar:10915/24421
network_acronym_str SEDICI
repository_id_str 1329
network_name_str SEDICI (UNLP)
spelling Spectral partitioning of random graphs with given expected degreesGoerdt, AndreasCoja-Oghlan, AminLanka, AndréCiencias Informáticasrandom graphspectral techniquesIt is a well established fact, that - in the case of classical random graphs like (variants of) Gn,p or random regular graphs - spectral methods yield efficient algorithms for clustering (e. g. colouring or bisection) problems. The theory of large networks emerging recently provides convincing evidence that such networks, albeit looking random in some sense, cannot sensibly be described by classical random graphs. A variety of new types of random graphs have been introduced. One of these types is characterized by the fact that we have a fixed expected degree sequence, that is for each vertex its expected degree is given. Recent theoretical work confirms that spectral methods can be successfully applied to clustering problems for such random graphs, too - provided that the expected degrees are not too small, in fact ≥ log<sup>6</sup> n. In this case however the degree of each vertex is concentrated about its expectation. We show how to remove this restriction and apply spectral methods when the expected degrees are bounded below just by a suitable constant. Our results rely on the observation that techniques developed for the classical sparse Gn,p random graph (that is p = c/n) can be transferred to the present situation, when we consider a suitably normalized adjacency matrix: We divide each entry of the adjacency matrix by the product of the expected degrees of the incident vertices. Given the host of spectral techniques developed for Gn,p this observation should be of independent interest.4th IFIP International Conference on Theoretical Computer ScienceRed de Universidades con Carreras en Informática (RedUNCI)2006-08info:eu-repo/semantics/conferenceObjectinfo:eu-repo/semantics/publishedVersionObjeto de conferenciahttp://purl.org/coar/resource_type/c_5794info:ar-repo/semantics/documentoDeConferenciaapplication/pdfhttp://sedici.unlp.edu.ar/handle/10915/24421enginfo:eu-repo/semantics/altIdentifier/isbn/0-387-34633-3info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/2.5/ar/Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Argentina (CC BY-NC-SA 2.5)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-29T10:55:50Zoai:sedici.unlp.edu.ar:10915/24421Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 10:55:51.055SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Spectral partitioning of random graphs with given expected degrees
title Spectral partitioning of random graphs with given expected degrees
spellingShingle Spectral partitioning of random graphs with given expected degrees
Goerdt, Andreas
Ciencias Informáticas
random graph
spectral techniques
title_short Spectral partitioning of random graphs with given expected degrees
title_full Spectral partitioning of random graphs with given expected degrees
title_fullStr Spectral partitioning of random graphs with given expected degrees
title_full_unstemmed Spectral partitioning of random graphs with given expected degrees
title_sort Spectral partitioning of random graphs with given expected degrees
dc.creator.none.fl_str_mv Goerdt, Andreas
Coja-Oghlan, Amin
Lanka, André
author Goerdt, Andreas
author_facet Goerdt, Andreas
Coja-Oghlan, Amin
Lanka, André
author_role author
author2 Coja-Oghlan, Amin
Lanka, André
author2_role author
author
dc.subject.none.fl_str_mv Ciencias Informáticas
random graph
spectral techniques
topic Ciencias Informáticas
random graph
spectral techniques
dc.description.none.fl_txt_mv It is a well established fact, that - in the case of classical random graphs like (variants of) Gn,p or random regular graphs - spectral methods yield efficient algorithms for clustering (e. g. colouring or bisection) problems. The theory of large networks emerging recently provides convincing evidence that such networks, albeit looking random in some sense, cannot sensibly be described by classical random graphs. A variety of new types of random graphs have been introduced. One of these types is characterized by the fact that we have a fixed expected degree sequence, that is for each vertex its expected degree is given. Recent theoretical work confirms that spectral methods can be successfully applied to clustering problems for such random graphs, too - provided that the expected degrees are not too small, in fact ≥ log<sup>6</sup> n. In this case however the degree of each vertex is concentrated about its expectation. We show how to remove this restriction and apply spectral methods when the expected degrees are bounded below just by a suitable constant. Our results rely on the observation that techniques developed for the classical sparse Gn,p random graph (that is p = c/n) can be transferred to the present situation, when we consider a suitably normalized adjacency matrix: We divide each entry of the adjacency matrix by the product of the expected degrees of the incident vertices. Given the host of spectral techniques developed for Gn,p this observation should be of independent interest.
4th IFIP International Conference on Theoretical Computer Science
Red de Universidades con Carreras en Informática (RedUNCI)
description It is a well established fact, that - in the case of classical random graphs like (variants of) Gn,p or random regular graphs - spectral methods yield efficient algorithms for clustering (e. g. colouring or bisection) problems. The theory of large networks emerging recently provides convincing evidence that such networks, albeit looking random in some sense, cannot sensibly be described by classical random graphs. A variety of new types of random graphs have been introduced. One of these types is characterized by the fact that we have a fixed expected degree sequence, that is for each vertex its expected degree is given. Recent theoretical work confirms that spectral methods can be successfully applied to clustering problems for such random graphs, too - provided that the expected degrees are not too small, in fact ≥ log<sup>6</sup> n. In this case however the degree of each vertex is concentrated about its expectation. We show how to remove this restriction and apply spectral methods when the expected degrees are bounded below just by a suitable constant. Our results rely on the observation that techniques developed for the classical sparse Gn,p random graph (that is p = c/n) can be transferred to the present situation, when we consider a suitably normalized adjacency matrix: We divide each entry of the adjacency matrix by the product of the expected degrees of the incident vertices. Given the host of spectral techniques developed for Gn,p this observation should be of independent interest.
publishDate 2006
dc.date.none.fl_str_mv 2006-08
dc.type.none.fl_str_mv info:eu-repo/semantics/conferenceObject
info:eu-repo/semantics/publishedVersion
Objeto de conferencia
http://purl.org/coar/resource_type/c_5794
info:ar-repo/semantics/documentoDeConferencia
format conferenceObject
status_str publishedVersion
dc.identifier.none.fl_str_mv http://sedici.unlp.edu.ar/handle/10915/24421
url http://sedici.unlp.edu.ar/handle/10915/24421
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/isbn/0-387-34633-3
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Argentina (CC BY-NC-SA 2.5)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Argentina (CC BY-NC-SA 2.5)
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
_version_ 1844615818093002752
score 13.070432