PageRank of Scale Free Growing Networks

Konstantin Avrachenkov (1) , Dmitri Lebedev (2)

1 MAESTRO - Models for the performance analysis and the control of networks
2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

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. 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.

Mots clés: PAGERANK; WEB GRAPH; GROWING SCALE FREE NETWORKS; PÓLYA-EGGENBERGER URN MODELS; POWER LAW; SCALE-FREE

Domaines: Autre [cs.OH]

Konstantin Avrachenkov, Dmitri Lebedev. PageRank of Scale Free Growing Networks. [Research Report] RR-5858, INRIA. 2006, pp.24. ⟨inria-00070168⟩