PageRank in Growing Scale Free Network Models

Dmitri Lebedev

LIX, Ecole Polytechnique


Résumé:

PageRank is one of the principle criteria according to which Google ranks Web pages. PageRank can be interpreted as a frequency of visiting a Web page by a random surfer and thus it reflects the popularity of a Web page. In the present work we find an analytical expression for the expected PageRank value in scale free network model as a function of the age of the growing network and the age of a particular node. Furthermore, we derive asymptotics that show that PageRank distribution is indeed close to a power law. The exponent of the theoretical power law matches very well the value found from measurements of the Web. Finally, our expressions give a mathematical insight for the choice of the Google constant.


[Dmitri Lebedev]
[LIX, Ecole Polytechnique]