Twitter和Wikipedia网络的PageRank概率的Poisson统计
Poisson statistics of PageRank probabilities of Twitter and Wikipedia networks
摘要：
我们使用量子混沌和随机矩阵理论的方法来分析有向网络中PageRank概率的统计涨落。在该方法中，有效能级由给定节点处的PageRank概率的对数给出。在标准的能级展开过程之后，我们建立了PageRank概率的最近间距分布由可积量子系统的典型泊松定律描述。我们的研究是为Twitter网络和三个网络的维基百科版本的英语，法语和德语。我们认为，由于水平排斥的情况下，附近节点的PageRank顺序可以很容易地互换。所得到的泊松定律意味着附近的PageRank概率作为随机独立变量波动。
英文摘要：
We use the methods of quantum chaos and Random Matrix Theory for analysis of statistical fluctuations of PageRank probabilities in directed networks. In this approach the effective energy levels are given by a logarithm of PageRank probability at a given node. After the standard energy level unfolding procedure we establish that the nearest spacing distribution of PageRank probabilities is described by the Poisson law typical for integrable quantum systems. Our studies are done for the Twitter network and three networks of Wikipedia editions in English, French and German. We argue that due to absence of level repulsion the PageRank order of nearby nodes can be easily interchanged. The obtained Poisson law implies that the nearby PageRank probabilities fluctuate as random independent variables.
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