Determining Factors Behind the PageRank Log-Log Plot

Abstract. We study the relation between PageRank and other parameters of information networks such as in-degree, out-degree, and the fraction of dangling nodes. We model this relation through a stochastic equation inspired by the original definition of PageRank. Further, we use the theory of regular variation to prove that PageRank and in-degree follow power laws with the same exponent. The difference between these two power laws is in a multiplicative constant, which depends mainly on the fraction of dangling nodes, average in-degree, the power law exponent, and the damping factor. The out-degree distribution has a minor effect, which we explicitly quantify. Finally, we propose a ranking scheme which does not depend on out-degrees. Keywords. PageRank, Power laws, Ranking algorithms, Stochastic equations, Web graph, Wikipedia

• Type: Conference
• Year: 2007
• Where: WAW
• Authors: Yana Volkovich, Nelly Litvak, Debora Donato
• Keywords: Algorithms, Follow Power Laws, Power Laws, Stochastic Equations, WAW 2007