有向网络中结构相关标度的相变
Phase transitions for scaling of structural correlations in directed networks
摘要：
分析复杂网络中的度-度依赖及其对网络过程的影响需要零模型，即生成不相关无标度网络的模型。然而，迄今为止，大多数模型显示出结构性的负相关性，由有限的尺寸效应引起的。我们分析了这些结构的负度度依赖的行为，使用基于秩的相关性措施，在定向擦除配置模型。我们得到的表达式的缩放作为一个函数的指数的分布。此外，我们表明，这种缩放经历了相变，其中一个区域表现出缩放相关的网络的自然截止，而另一个区域的缩放类似于不相关的网络的结构截止。通过建立这些结构依赖关系的收敛速度，我们能够评估有限复杂网络上的度-度依赖关系的统计显著性，与有向擦除配置模型生成的网络相比。
英文摘要：
Analysis of degree-degree dependencies in complex networks, and their impact on processes on networks requires null models, i.e. models that generate uncorrelated scale-free networks. Most models to date however show structural negative dependencies, caused by finite size effects. We analyze the behavior of these structural negative degree-degree dependencies, using rank based correlation measures, in the directed Erased Configuration Model. We obtain expressions for the scaling as a function of the exponents of the distributions. Moreover, we show that this scaling undergoes a phase transition, where one region exhibits scaling related to the natural cut-off of the network while another region has scaling similar to the structural cut-off for uncorrelated networks. By establishing the speed of convergence of these structural dependencies we are able to asses statistical significance of degree-degree dependencies on finite complex networks when compared to networks generated by the directed Erased Configuration Model.
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