Alibaba Research Center for Complexity Sciences, Alibaba Business School, Hangzhou Normal University, Hangzhou 311121, PR China.
Department of Physics, University of Fribourg, 1700 Fribourg, Switzerland.
Phys Rev E. 2018 May;97(5-1):052311. doi: 10.1103/PhysRevE.97.052311.
Complex networks are often used to represent systems that are not static but grow with time: People make new friendships, new papers are published and refer to the existing ones, and so forth. To assess the statistical significance of measurements made on such networks, we propose a randomization methodology-a time-respecting null model-that preserves both the network's degree sequence and the time evolution of individual nodes' degree values. By preserving the temporal linking patterns of the analyzed system, the proposed model is able to factor out the effect of the system's temporal patterns on its structure. We apply the model to the citation network of Physical Review scholarly papers and the citation network of US movies. The model reveals that the two data sets are strikingly different with respect to their degree-degree correlations, and we discuss the important implications of this finding on the information provided by paradigmatic node centrality metrics such as indegree and Google's PageRank. The randomization methodology proposed here can be used to assess the significance of any structural property in growing networks, which could bring new insights into the problems where null models play a critical role, such as the detection of communities and network motifs.
人们结交新朋友，新论文发表并引用现有的论文，等等。为了评估在这种网络上进行的测量的统计显著性，我们提出了一种随机化方法——一种尊重时间的零模型，它既保留了网络的度序列，也保留了单个节点度值的时间演化。通过保留所分析系统的时间链接模式，所提出的模型能够消除系统的时间模式对其结构的影响。我们将该模型应用于《物理评论》学术论文的引文网络和美国电影的引文网络。该模型表明，这两个数据集在它们的度-度相关性方面存在显著差异，我们讨论了这一发现对度中心性指标（如入度和谷歌的 PageRank）所提供的信息的重要意义。这里提出的随机化方法可用于评估增长网络中任何结构属性的显著性，这可能会为在零模型发挥关键作用的问题（如社区和网络基元的检测）带来新的见解。
