Issue
EPL
Volume 88, Number 4, November 2009
Article Number 48002
Number of page(s) 5
Section Interdisciplinary Physics and Related Areas of Science and Technology
DOI http://dx.doi.org/10.1209/0295-5075/88/48002
Published online 20 November 2009
EPL, 88 (2009) 48002
DOI: 10.1209/0295-5075/88/48002

PageRank equation and localization in the WWW

N. Perra1, 2, 3, V. Zlatić4, 5, A. Chessa1, 2, C. Conti6, 7, D. Donato8 and G. Caldarelli2, 4, 7

1   Department of Physics, SLACS-CNR University of Cagliari - S.P. Monserrato-Sestu Km 0.700, 09042 Cagliari, Italy, EU
2   Linkalab, Complex Systems Computational Laboratory - 09100 Cagliari Italy, EU
3   Center for Complex Networks and Systems Research, School of Informatics and Computing, Indiana University Bloomington, IN, USA
4   Centre SMC CNR-INFM, Department of Physics, University “Sapienza” - P.le Moro 5, 00185 Rome, Italy, EU
5   Theoretical Physics Division, Rudjer Boskovic Institute - P.O. Box 180, HR-10002 Zagreb, Croatia
6   Centre SOFT INFM-CNR, Department of Physics, University “Sapienza” - P.le Moro 5, 00185 Rome, Italy, EU
7   Institute for Complex Systems ISC-CNR - Via dei Taurini 19, 00185 Rome, Italy, EU
8   Yahoo! Research - Avinguda Diagonal 177, 8th floor, 08018 Barcelona, Spain, EU

nicolaperra@gmail.com

received 17 August 2009; accepted in final form 23 October 2009; published November 2009
published online 20 November 2009

Abstract
We show that the PageRank in a network can be represented as the solution of a differential equation discretized over a directed graph. By exploiting a formal relationship with the time-independent Schrödinger equation it is possible to interpret hub formation and related phenomena as a wave-like localization process in the presence of disorder and trapping potentials. The result opens new perspectives in the physics of networks with interdisciplinary connections and opens the way to the employment of various mathematical techniques to the analysis of self-organization in structured systems. Applications are envisaged in the World-Wide Web, traffic, social and biological networks.

PACS
89.75.Fb - Structures and organization in complex systems.
05.10.-a - Computational methods in statistical physics and nonlinear dynamics.
71.23.-k - Electronic structure of disordered solids.

© EPLA 2009