Graphicality conditions for general scale-free complex networks and their application to visibility graphs.
Graphicality conditions for general scale-free complex networks and their application to visibility graphs.
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DOI：
10.1103/physreve.94.012314
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发表时间：
2016-04
期刊：
影响因子：
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通讯作者：
Miguel A. Rodríguez
中科院分区：
文献类型：
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作者：
Miguel A. Rodríguez
我们获得了一般类型的无标度网络的图形条件。在一般情况下获得了对于不相关网络获得的相同条件。然后建立将度分布的指数γ与截止指数κ相关的上限，因为κ<1/γ。该界限对于在 γ≤2 范围内具有明确定义的幂律度分布的所有网络都有效。由于不满足这些条件，因此对最近由持续分数布朗运动（fBm）过程引起的可见性网络的一些数值研究进行了回顾。因此，假设了度分布的指数 γ 和 fBm 过程的 Hurst 指数 H 之间的新关系 γ⪅1/H。
We obtain graphicality conditions for general types of scale-free networks. The same conditions obtained for uncorrelated networks are obtained in the general case. Then an upper bound relating γ, the exponent of the degree distribution, with the cutoff exponent κ, as κ<1/γ is established. This bound is valid for all networks with a well-defined power-law degree distribution in the range γ≤2. Some recent numerical research on visibility networks arising from persistent fractional Brownian motion (fBm) processes are reviewed since they do not fulfill these conditions. As a consequence, a new relationship between the exponent γ of the degree distribution and the Hurst exponent H of the fBm process, γ⪅1/H, is postulated.