PageRank of Scale-Free Growing Networks

PageRank is one of the principle criteria according to which Google ranks webpages. PageRank can be interpreted as a frequency of webpage visits by a random surfer, and thus it reflects the popularity of a webpage. In the present work we find an analytical expression for the expected PageRank value in a scale-free growing network model as a function of the age of the growing network and the age of a particular node. Then, we derive asymptotics that show that PageRank follows closely a power law in the middle range of its values. The exponent of the theoretical power law matches very well the value found from measurements of the World Wide Web. Finally, we provide a mathematical insight for the choice of the damping factor in PageRank definition.