2010/02/17 by Bertrand Georgeot, B. Georgeot, Olivier Giraud +3 · 1 citation
Chemistry · Computer Science · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Computer science #Eigenvalues and eigenvectors #Homogeneous #Machine learning #Materials science #Mathematics #Matrix (chemical analysis) #Molecular spectroscopy and chirality #Opinion Dynamics and Social Influence #PageRank #Physics #Quantum mechanics #Spectral properties #Stability (learning theory) #Statistical physics #Theoretical computer science #Vocabulary #cs.IR
paper · pdf · doi:10.1103/physreve.81.056109
published as Phys. Rev. E 81, 056109 (2010) · 8 pages, 12 figures, research done at http://www.quantware.ups-tlse.fr
arxiv created 2010/02/17 · openalex publication_date 2010/05/25 · arxiv updated 2010/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study numerically the spectrum and eigenstate properties of the Google matrix of various examples of directed networks such as vocabulary networks of dictionaries and university World Wide Web networks. The spectra have gapless structure in the vicinity of the maximal eigenvalue for Google damping parameter α equal to unity. The vocabulary networks have relatively homogeneous spectral density, while university networks have pronounced spectral structures which change from one university to another, reflecting specific properties of the networks. We also determine specific properties of eigenstates of the Google matrix, including the PageRank. The fidelity of the PageRank is proposed as a characterization of its stability.