N. Perra et al 2009 EPL 88 48002 doi:10.1209/0295-5075/88/48002
N. Perra1,2,3, V. Zlatić4,5, A. Chessa1,2, C. Conti6,7, D. Donato8 and G. Caldarelli2,4,7
Show affiliationsWe 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.
71.23.-k Electronic structure of disordered solids
89.75.Fb Structures and organization in complex systems
05.10.-a Computational methods in statistical physics and nonlinear dynamics
Issue 4 (November 2009)
Received 17 August 2009, accepted for publication 23 October 2009
Published 20 November 2009
N. Perra et al 2009 EPL 88 48002
A Richter 2006 Phys. Scr. 2006 167
A Richter 2005 J. Phys.: Conf. Ser. 20 13
Jie Yang et al 2008 Supercond. Sci. Technol. 21 082001
Alessandro Magni et al J. Stat. Mech. (2009) P01020
Zénó Farkas et al 2003 J. Phys.: Condens. Matter 15 S1767
Kurusch Ebrahimi-Fard and Dirk Kreimer 2005 J. Phys. A: Math. Gen. 38 R385
Marc Joyeux and Ana-Maria Florescu 2009 J. Phys.: Condens. Matter 21 034101
Marc Joyeux 1996 J. Phys. A: Math. Gen. 29 5963
L Blanchet and G Schafer 1993 Class. Quantum Grav. 10 2699