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, G., Graña, M., Pinasco, J.P.
Formato: JOUR
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: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 todo:paper_14346028_v53_n3_p381_Acosta
record_format dspace
spelling todo:paper_14346028_v53_n3_p381_Acosta2023-10-03T16:14:32Z Condition numbers and scale free graphs Acosta, G. Graña, M. Pinasco, J.P. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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, G.
Graña, M.
Pinasco, J.P.
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.
format JOUR
author Acosta, G.
Graña, M.
Pinasco, J.P.
author_facet Acosta, G.
Graña, M.
Pinasco, J.P.
author_sort Acosta, G.
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
url http://hdl.handle.net/20.500.12110/paper_14346028_v53_n3_p381_Acosta
work_keys_str_mv AT acostag conditionnumbersandscalefreegraphs
AT granam conditionnumbersandscalefreegraphs
AT pinascojp conditionnumbersandscalefreegraphs
_version_ 1807317005927186432

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