Distribution of PageRank Mass Among Principle Components of the Web

TL;DR

This paper analyzes how PageRank distributes among Web graph components as the damping factor varies, revealing issues with dead-ends and suggesting a smaller damping factor to improve fairness.

Contribution

It introduces a singular perturbation approach to study PageRank distribution and highlights the impact of the damping factor on different Web graph components.

Findings

PageRank share of IN and SCC remains high for large damping factors.

Dead-ends receive unfairly high PageRank when damping factor approaches one.

Using a damping factor of 1/2 mitigates the dead-end problem.

Abstract

We study the PageRank mass of principal components in a bow-tie Web Graph, as a function of the damping factor c. Using a singular perturbation approach, we show that the PageRank share of 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 goes to one. However, a detailed study of the OUT component reveals the presence ``dead-ends'' (small groups of pages linking only to each other) that receive an unfairly high ranking when c is close to one. We argue that this problem can be mitigated by choosing c as small as 1/2.