PageRank of Scale-Free Growing Networks

13 years 4 months ago

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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

Konstantin Avrachenkov, Dmitri Lebedev

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