Internet Mathematics

A Singular Perturbation Approach for Choosing the PageRank Damping Factor

Konstantin Avrachenkov, Nelly Litvak, and Kim Son Pham

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Abstract

We study the PageRank mass of principal components in a bow-tie web graph as a function of the damping factor $c$. It is known that the web graph can be divided into three principal components: SCC, IN, and OUT. The giant strongly connected component (SCC) contains a large group of pages having a hyperlink path connecting them. The pages in the IN (OUT) component have a path to (from) the SCC, but not back. Using a singular perturbation approach, we show that the PageRank share of the IN and SCC components remains high even for very large values of the damping factor, in spite of the fact that it drops to zero when $c$ tends to one. However, a detailed study of the OUT component reveals the presence of ``dead ends'' (small groups of pages linking only to each other) that receive an unfairly high ranking when $c$ is close to $1$. We argue that this problem can be mitigated by choosing $c$ as small as $\frac12$.

Article information

Source
Internet Math., Volume 5, Number 1-2 (2008), 47-70.

Dates
First available in Project Euclid: 25 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.im/1259158597

Mathematical Reviews number (MathSciNet)
MR2560262

Zentralblatt MATH identifier
1206.68349

Citation

Avrachenkov, Konstantin; Litvak, Nelly; Pham, Kim Son. A Singular Perturbation Approach for Choosing the PageRank Damping Factor. Internet Math. 5 (2008), no. 1-2, 47--70. https://projecteuclid.org/euclid.im/1259158597


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