Generating hierarchial scale-free graphs from fractals
Generating hierarchial scale-free graphs from fractals
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DOI：
10.1016/j.chaos.2011.05.012
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发表时间：
2011-04
影响因子：
7.8
通讯作者：
J. Komjáthy;K. Simon
中科院分区：
文献类型：
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作者：
J. Komjáthy;K. Simon
受E.Ravasz，A.-L.Barabási和T.Vicsek的层次网络模型的启发，我们引入了由图有向自相似分形Λ派生的确定性无标度网络。通过严格的数学结果，我们验证了我们的模型捕捉到了许多真实网络的一些最重要的特征：无标度和高聚集性。我们还证明了直径是系统大小的对数。指出了度分布的幂指数与其内在的几何度量理论性质之间的联系。利用我们的(确定性)分形Λ，我们生成了具有相似性质的随机图序列。
Motivated by the hierarchial network model of E. Ravasz, A.-L. Barabási, 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. We point out a connection between the power law exponent of the degree distribution and some intrinsic geometric measure theoretical properties of the underlying fractal. Using our (deterministic) fractal Λ we generate random graph sequence sharing similar properties.