复杂网络的分形边界
Fractal Boundaries of Complex Networks
摘要：
我们引入了复杂网络边界的概念，即距离网络中给定节点的平均距离大于平均距离的节点集。研究了复杂网络边界节点的统计性质。我们发现，无论是Erdös-Rényi和无标度模型网络，以及一些真正的网络，边界具有分形特性。具体地，边界节点的数量{ \it B}遵循幂律概率密度函数，其缩放为$B^{-2}$。由边界节点形成的簇是具有分形维数$d_{f} \approx 2$的分形。我们提出了分析和数值证据支持这些结果的广泛的网络。我们的发现暗示了传染病传播的潜在应用。
英文摘要：
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 Erdös-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 {\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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
