PageRank of Scale-Free Growing Networks

PageRank is one of the principle criteria according to which Google ranks Web pages. PageRank can be interpreted as a frequency of Web page visits 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 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 shows 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 Web. Finally, we provide a mathematical insight for the choice of the damping factor in PageRank definition. Key Words: PageRank, Web Graph, Growing scale free networks, P´olya-Eggenberger urn models, Power law

• Type: Journal
• Year: 2007
• Where: IM
• Authors: Konstantin Avrachenkov, Dmitri Lebedev
• Keywords: IM 2007, PageRank, Power Law, Web Page