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.
%0 Journal Article
%1 0295-5075-88-4-48002
%A Perra, N.
%A Zlatić, V.
%A Chessa, A.
%A Conti, C.
%A Donato, D.
%A Caldarelli, G.
%D 2009
%J EPL (Europhysics Letters)
%K imported myown
%N 4
%P 48002
%T PageRank equation and localization in the WWW
%U http://stacks.iop.org/0295-5075/88/i=4/a=48002
%V 88
%X 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.
@article{0295-5075-88-4-48002,
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 Schr{\"o}dinger 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.},
added-at = {2016-08-09T20:29:14.000+0200},
author = {Perra, N. and Zlati{\'c}, V. and Chessa, A. and Conti, C. and Donato, D. and Caldarelli, G.},
biburl = {https://www.bibsonomy.org/bibtex/26dbc04fc839a84bb9c893adf8776a4aa/nonlinearxwaves},
interhash = {1e39e63c2e38d3bf5b76ee658e3134a1},
intrahash = {6dbc04fc839a84bb9c893adf8776a4aa},
journal = {EPL (Europhysics Letters)},
keywords = {imported myown},
number = 4,
pages = 48002,
timestamp = {2016-08-09T20:35:45.000+0200},
title = {PageRank equation and localization in the WWW},
url = {http://stacks.iop.org/0295-5075/88/i=4/a=48002},
volume = 88,
year = 2009
}