Spectral properties of Google matrix of Wikipedia and other networks

TL;DR

This paper analyzes the spectral properties of the Google matrix for Wikipedia and other networks, revealing community structures and information flow patterns through eigenvalue distributions and rank correlations.

Contribution

It introduces a spectral analysis approach using the Arnoldi method to uncover community structures and information flow differences in real-world networks.

Findings

Eigenstates with significant eigenvalues are associated with network communities.

Eigenvalue distribution in the complex plane reveals structural properties.

Correlation between PageRank and CheiRank distinguishes information organization.

Abstract

We study the properties of eigenvalues and eigenvectors of the Google matrix of the Wikipedia articles hyperlink network and other real networks. With the help of the Arnoldi method we analyze the distribution of eigenvalues in the complex plane and show that eigenstates with significant eigenvalue modulus are located on well defined network communities. We also show that the correlator between PageRank and CheiRank vectors distinguishes different organizations of information flow on BBC and Le Monde web sites.