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
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/24421
Ver los metadatos del registro completo
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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 |
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dc.identifier.none.fl_str_mv |
http://sedici.unlp.edu.ar/handle/10915/24421 |
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http://sedici.unlp.edu.ar/handle/10915/24421 |
dc.language.none.fl_str_mv |
eng |
language |
eng |
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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) |
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openAccess |
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http://creativecommons.org/licenses/by-nc-sa/2.5/ar/ Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Argentina (CC BY-NC-SA 2.5) |
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