Fractal boundaries of complex networks

被引：56

作者：

Shao, Jia ^{[1
,2
]}

Buldyrev, Sergey V. ^{[1
,2
,3
]}

Cohen, Reuven ^{[4
]}

Kitsak, Maksim ^{[1
,2
]}

Havlin, Shlomo ^{[5
,6
]}

Stanley, H. Eugene ^{[1
,2
]}

机构：

[1] Boston Univ, Ctr Polymer Studies, Boston, MA 02215 USA

[2] Boston Univ, Dept Phys, Boston, MA 02215 USA

[3] Yeshiva Univ, Dept Phys, New York, NY 10033 USA

[4] Bar Ilan Univ, Dept Math, IL-52900 Ramat Gan, Israel

[5] Bar Ilan Univ, Minerva Ctr, IL-52900 Ramat Gan, Israel

[6] Bar Ilan Univ, Dept Phys, IL-52900 Ramat Gan, Israel

来源：

EPL | 2008年 / 84卷 / 04期

基金：

以色列科学基金会;

关键词：

D O I：

10.1209/0295-5075/84/48004

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We introduce the concept of the boundary of a complex network as the set of nodes at distance larger than the mean distance from a given node in the network. We study the statistical properties of the boundary nodes seen from a given node of complex networks. We find that for both Erdos-Renyi and scale-free model networks, as well as for several real networks, the boundaries have fractal properties. In particular, the number of boundaries nodes B follows a power law probability density function which scales as B-2. The clusters formed by the boundary nodes seen from a given node are fractals with a fractal dimension d(f) approximate to 2. We present analytical and numerical evidences supporting these results for a broad class of networks. Copyright (c) EPLA, 2008

引用

页数：6

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