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arXiv · 0804.1968

Fractal Boundaries of Complex Networks

Jia Shao·Sergey V. Buldyrev·Reuven Cohen·Maksim Kitsak·Shlomo Havlin·H. Eugene Stanley
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Abstract

We introduce the concept of boundaries 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 boundaries nodes of complex networks. We find that for both Erd\"{o}s-R\'{e}nyi and scale-free model networks, as well as for several real networks, the boundaries have fractal properties. In particular, the number of boundaries nodes {\it B} follows a power-law probability density function which scales as $B^{-2}$. The clusters formed by the boundary nodes are fractals with a fractal dimension $d_{f} \approx 2$. We present analytical and numerical evidence supporting these results for a broad class of networks. Our findings imply potential applications for epidemic spreading.

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BibTeXRIS

Jia Shao, Sergey V. Buldyrev, Reuven Cohen, Maksim Kitsak, Shlomo Havlin, H. Eugene Stanley. 2008-04-11. Fractal Boundaries of Complex Networks. https://doi.org/10.1209/0295-5075/84/48004

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