Condition numbers and scale free graphs

被引：4

作者：

Acosta, G.

Grana, M.

Pinasco, J. P.

机构：

[1] Univ Nacl Gral Sarmiento, Inst Ciencias, RA-1613 Buenos Aires, DF, Argentina

[2] Univ Buenos Aires, Dept Math, FCE&N, RA-1428 Buenos Aires, DF, Argentina

来源：

EUROPEAN PHYSICAL JOURNAL B | 2006年 / 53卷 / 03期

关键词：

Least squares approximations - Mathematical models - Matrix algebra - Number theory - Numerical methods;

D O I：

10.1140/epjb/e2006-00377-4

中图分类号：

O469 [凝聚态物理学];

学科分类号：

070205 ;

摘要：

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.

引用

页码：381 / 385

页数：5

共 24 条

[1]

ACHLIOPTAS D, 2005, P STOC, P45105

[2] Statistical mechanics of complex networks [J].

Albert, R ;

Barabási, AL .

REVIEWS OF MODERN PHYSICS, 2002, 74 (01) :47-97

[3] Emergence of scaling in random networks [J].

Barabási, AL ;

Albert, R .

SCIENCE, 1999, 286 (5439) :509-512

[4]

Belsley D. A., 1976, 154 NAT BUR EC RES

[5]

Belsley DA., 1991, Conditioning Diagnostics: Collinearity and Weak Data in Regression

[6]

CHATTERJEE S, 1991, WILEY SERIES PROBABI

[7]

Chen Q., 2002, P IEEE INFOCOM

[8] Accuracy and scaling phenomena in Internet mapping [J].

Clauset, A ;

Moore, C .

PHYSICAL REVIEW LETTERS, 2005, 94 (01)

[9] Statistical theory of Internet exploration -: art. no. 036135 [J].

Dall'Asta, L ;

Alvarez-Hamelin, I ;

Barrat, A ;

Vázquez, A ;

Vespignani, A .

PHYSICAL REVIEW E, 2005, 71 (03)

[10] Size-dependent degree distribution of a scale-free growing network [J].

Dorogovtsev, S.N. ;

Mendes, J.F.F. ;

Samukhin, A.N. .

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2001, 63 (6 I) :1-062101

← 1 2 3 →