All Scale-Free Networks Are Sparse

被引：110

作者：

Del Genio, Charo I. ^{[1
]}

Gross, Thilo ^{[1
]}

Bassler, Kevin E. ^{[2
,3
]}

机构：

[1] Max Planck Inst Phys Komplexer Syst, D-01187 Dresden, Germany

[2] Univ Houston, Dept Phys, Houston, TX 77204 USA

[3] Univ Houston, Houston Sci Ctr 202, Texas Ctr Superconduct, Houston, TX 77204 USA

来源：

PHYSICAL REVIEW LETTERS | 2011年 / 107卷 / 17期

关键词：

1ST-ORDER PHASE-TRANSITIONS; COMPLEX NETWORKS; INTERNET; WEB;

D O I：

10.1103/PhysRevLett.107.178701

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We study the realizability of scale-free networks with a given degree sequence, showing that the fraction of realizable sequences undergoes two first-order transitions at the values 0 and 2 of the power-law exponent. We substantiate this finding by analytical reasoning and by a numerical method, proposed here, based on extreme value arguments, which can be applied to any given degree distribution. Our results reveal a fundamental reason why large scale-free networks without constraints on minimum and maximum degree must be sparse.

引用

页数：4

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