Volume 84, Number 4, November 2008
|Number of page(s)||6|
|Section||Interdisciplinary Physics and Related Areas of Science and Technology|
|Published online||21 November 2008|
Fractal boundaries of complex networks
Center for Polymer Studies and Department of Physics, Boston University - Boston, MA 02215, USA
2 Department of Physics, Yeshiva University - 500 West 185th Street, New York, NY 10033, USA
3 Department of Mathematics, Bar-Ilan University - 52900 Ramat-Gan, Israel
4 Minerva Center and Department of Physics, Bar-Ilan University - 52900 Ramat-Gan, Israel
Corresponding author: firstname.lastname@example.org
Accepted: 16 October 2008
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 Erdős-Rényi 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 df ≈ 2. We present analytical and numerical evidences supporting these results for a broad class of networks.
PACS: 89.75.Hc – Networks and genealogical trees / 89.75.-k – Complex systems / 64.60.aq – Networks
© EPLA, 2008
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