# 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.