Eur. Phys. J. B 53, 381-385 (2006)
https://doi.org/10.1140/epjb/e2006-00377-4

Condition numbers and scale free graphs

¹ Instituto de Ciencias, Univ. Nac. de Gral. Sarmiento, J.M. Gutierrez 1150, (1613) Los Polvorines, Buenos Aires, Argentina
² Depto de Matematicas, FCEyN, Universidad de Buenos Aires, Ciudad Universitaria, Pab. 1 (1428), Ciudad de Buenos Aires, Argentina

Corresponding author: ^a jpinasco@ungs.edu.ar

Received: 3 February 2006
Revised: 16 August 2006
Published online: 18 October 2006

Abstract

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.