Poisson Statistics of Pagerank Probabilities of Twitter and Wikipedia Networks

Poisson Statistics of Pagerank Probabilities of Twitter and Wikipedia Networks - scientific work related to Wikipedia quality published in 2014, written by Klaus M. Frahm and Dima L. Shepelyansky.

Overview

Authors 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 authors establish that the nearest spacing distribution of PageRank probabilities is described by the Poisson law typical for integrable quantum systems. Authors studies are done for the Twitter network and three networks of Wikipedia editions in English, French and German. Authors 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.