Condition numbers and scale free graphs

In this work we study the condition number of the least square matrix corresponding to scale free networks. We compute a theoretical lower bound of the condition number which proves that they are ill conditioned. Also, we analyze several matrices from networks generated with Linear Preferential Atta...

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Detalles Bibliográficos
Autores principales:	Acosta Rodriguez, Gabriel, Graña, Matías Alejo, Pinasco, Juan Pablo
Publicado:	2006
Materias:	Least squares approximations Mathematical models Matrix algebra Number theory Numerical methods Edges models Least square methods Power law exponents Scale free networks Graph theory
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14346028_v53_n3_p381_Acosta http://hdl.handle.net/20.500.12110/paper_14346028_v53_n3_p381_Acosta
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_14346028_v53_n3_p381_Acosta
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spelling	paper:paper_14346028_v53_n3_p381_Acosta2023-06-08T16:14:36Z Condition numbers and scale free graphs Acosta Rodriguez, Gabriel Graña, Matías Alejo Pinasco, Juan Pablo Least squares approximations Mathematical models Matrix algebra Number theory Numerical methods Edges models Least square methods Power law exponents Scale free networks Graph theory In this work we study the condition number of the least square matrix corresponding to scale free networks. We compute a theoretical lower bound of the condition number which proves that they are ill conditioned. Also, we analyze several matrices from networks generated with Linear Preferential Attachment, Edge Redirection and Attach to Edges models, showing that it is very difficult to compute the power law exponent by the least square method due to the severe lost of accuracy expected from the corresponding condition numbers. © EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006. Fil:Acosta, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Graña, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Pinasco, J.P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2006 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14346028_v53_n3_p381_Acosta http://hdl.handle.net/20.500.12110/paper_14346028_v53_n3_p381_Acosta
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Least squares approximations Mathematical models Matrix algebra Number theory Numerical methods Edges models Least square methods Power law exponents Scale free networks Graph theory
spellingShingle	Least squares approximations Mathematical models Matrix algebra Number theory Numerical methods Edges models Least square methods Power law exponents Scale free networks Graph theory Acosta Rodriguez, Gabriel Graña, Matías Alejo Pinasco, Juan Pablo Condition numbers and scale free graphs
topic_facet	Least squares approximations Mathematical models Matrix algebra Number theory Numerical methods Edges models Least square methods Power law exponents Scale free networks Graph theory
description	In this work we study the condition number of the least square matrix corresponding to scale free networks. We compute a theoretical lower bound of the condition number which proves that they are ill conditioned. Also, we analyze several matrices from networks generated with Linear Preferential Attachment, Edge Redirection and Attach to Edges models, showing that it is very difficult to compute the power law exponent by the least square method due to the severe lost of accuracy expected from the corresponding condition numbers. © EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006.
author	Acosta Rodriguez, Gabriel Graña, Matías Alejo Pinasco, Juan Pablo
author_facet	Acosta Rodriguez, Gabriel Graña, Matías Alejo Pinasco, Juan Pablo
author_sort	Acosta Rodriguez, Gabriel
title	Condition numbers and scale free graphs
title_short	Condition numbers and scale free graphs
title_full	Condition numbers and scale free graphs
title_fullStr	Condition numbers and scale free graphs
title_full_unstemmed	Condition numbers and scale free graphs
title_sort	condition numbers and scale free graphs
publishDate	2006
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14346028_v53_n3_p381_Acosta http://hdl.handle.net/20.500.12110/paper_14346028_v53_n3_p381_Acosta
work_keys_str_mv	AT acostarodriguezgabriel conditionnumbersandscalefreegraphs AT granamatiasalejo conditionnumbersandscalefreegraphs AT pinascojuanpablo conditionnumbersandscalefreegraphs
_version_	1768544006811156480

Condition numbers and scale free graphs

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