由分形生成层次无标度图
Generating hierarchial scale free graphs from fractals
摘要：
受E. Ravasz，A. L. Barabasi和T. Vicsek，我们介绍了确定性的无标度网络来自一个图形导向的自相似分形$Λ$。通过严格的数学结果，我们验证了我们的模型捕获了许多真实网络的一些最重要的特征：无标度和高聚类特性。我们还证明了直径是系统大小的对数。使用我们的（确定性）分形$Λ$，我们产生随机图序列共享类似的属性。
英文摘要：
Motivated by the hierarchial network model of E. Ravasz, A.-L. Barabasi, and T. Vicsek, we introduce deterministic scale-free networks derived from a graph directed self-similar fractal $Λ$. With rigorous mathematical results we verify that our model captures some of the most important features of many real networks: the scale free and the high clustering properties. We also prove that the diameter is the logarithm of the size of the system. Using our (deterministic) fractal $Λ$ we generate random graph sequence sharing similar properties.
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