发表机构
Ibaraki University; Central European University; National Institute of Technology, Asahikawa College（茨城大学; 中欧大学; 旭川工业高等专门学校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究揭示了无标度随机网络中长程度相关性与分形性的联系，通过渗流阈值下的分析推导出球体积的度依赖结构交叉，并用临界分支过程解释，且在实证分形网络中得到验证。
AI 中文摘要
我们研究了无标度随机网络中长程度相关性与分形性之间的关系。通过分析渗流阈值（此时巨分量出现）下无标度随机网络中的度相关性，我们推导出球体积 $\tilde{\nu}_k(l)$，其定义为从度为 $k$ 的根节点出发距离 $l$ 内的平均节点数。所得表达式预测了一个依赖于度的结构交叉。对于 $l\ll k^{1/(\df-1)}$，球体积按 $\tilde{\nu}_k(l)\sim kl$ 增长；而对于 $l\gg k^{1/(\df-1)}$，则交叉到全局分形标度 $\tilde{\nu}_k(l)\sim l^{\df}$。这里，$\df$ 是临界无标度随机网络的分形维数。我们进一步表明，这种结构交叉可以自然地通过临界分支过程来理解，并且在经验分形网络中也观察到这一现象。
英文摘要
We investigate the relationship between long-range degree correlations and fractality in scale-free random networks. By analyzing degree correlations in scale-free random networks at the percolation threshold, at which a giant component emerges, we derive the ball volume $\tildeν_k(l)$, defined as the average number of nodes within distance $l$ from a root node with degree $k$. The resulting expression predicts a degree-dependent structural crossover. For $l\ll k^{1/(\df-1)}$, the ball volume grows as $\tildeν_k(l)\sim kl$, whereas for $l\gg k^{1/(\df-1)}$, it crosses over to the global fractal scaling $\tildeν_k(l)\sim l^{\df}$. Here, $\df$ is the fractal dimension of critical scale-free random networks. We further show that the structural crossover can be naturally understood in terms of critical branching processes and is also observed in empirical fractal networks.
Comments9 pages, 6 figures
