PageRank in Scale-Free Random Graphs

We analyze the distribution of PageRank on a directed configuration model and show that as the size of the graph grows to infinity, the PageRank of a randomly chosen node can be closely approximated by the PageRank of the root node of an appropriately constructed tree. This tree approximation is in turn related to the solution of a linear stochastic fixed-point equation that has been thoroughly studied in the recent literature.

[1]  Predrag R. Jelenkovic,et al.  Implicit Renewal Theorem for Trees with General Weights , 2010, 1012.2165.

[2]  Hector Garcia-Molina,et al.  Combating Web Spam with TrustRank , 2004, VLDB.

[3]  Sergey Brin,et al.  The Anatomy of a Large-Scale Hypertextual Web Search Engine , 1998, Comput. Networks.

[4]  Ningyuan Chen,et al.  Directed Random Graphs with given Degree Distributions , 2012, 1207.2475.

[5]  Ewa Damek,et al.  Precise tail index of fixed points of the two-sided smoothing transform , 2012, 1206.3970.

[6]  Predrag R. Jelenkovic,et al.  Information ranking and power laws on trees , 2009, Advances in Applied Probability.

[7]  N. Litvak,et al.  Asymptotic analysis for personalized Web search , 2010, Advances in Applied Probability.

[8]  Werner R. W. Scheinhardt,et al.  In-Degree and PageRank: Why Do They Follow Similar Power Laws? , 2007, Internet Math..

[9]  Amy Nicole Langville,et al.  Google's PageRank and beyond - the science of search engine rankings , 2006 .

[10]  Nelly Litvak,et al.  Ranking Algorithms on Directed Configuration Networks , 2014, 1409.7443.

[11]  Gerold Alsmeyer,et al.  Fixed points of the smoothing transform: two-sided solutions , 2010, Probability Theory and Related Fields.

[12]  Ludo Waltman,et al.  The relation between Eigenfactor, audience factor, and influence weight , 2010 .

[13]  Sergei Maslov,et al.  Finding scientific gems with Google's PageRank algorithm , 2006, J. Informetrics.

[14]  Fan Chung Graham,et al.  Local Graph Partitioning using PageRank Vectors , 2006, 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06).

[15]  Konstantin Avrachenkov,et al.  PageRank of Scale-Free Growing Networks , 2006, Internet Math..

[16]  Debora Donato,et al.  Determining Factors Behind the PageRank Log-Log Plot , 2007, WAW.

[17]  Predrag R. Jelenkovic,et al.  Implicit Renewal Theory and Power Tails on Trees , 2010, Advances in Applied Probability.

[18]  Mariana Olvera-Cravioto,et al.  Tail behavior of solutions of linear recursions on trees , 2011, 1108.3809.

[19]  Remco van der Hofstad,et al.  Random Graphs and Complex Networks , 2016, Cambridge Series in Statistical and Probabilistic Mathematics.

[20]  Eli Upfal,et al.  Using PageRank to Characterize Web Structure , 2002, COCOON.