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
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页数：6
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