PageRank for evolving link structures

TL;DR

This paper investigates how PageRank scores evolve in dynamic link structures, analyzing simple graph models and deriving explicit formulas to understand the impact of structural changes on rankings.

Contribution

It provides a detailed analysis of PageRank behavior in evolving link structures, including explicit formulas for simple graphs and insights into dynamic changes.

Findings

Explicit formulas for PageRank in simple structures

Behavior of PageRank under system modifications

Analysis of normalized and non-normalized PageRank

Abstract

In this article we will look at the PageRank algorithm used as part of the ranking process of different Internet pages in search engines by for example Google. This article has its main focus in the understanding of the behavior of PageRank as the system dynamically changes either by contracting or expanding such as when adding or subtracting nodes or links or groups of nodes or links. In particular we will take a look at link structures consisting of a line of nodes or a complete graph where every node links to all others. We will look at PageRank as the solution of a linear system of equations and do our examination in both the ordinary normalized version of PageRank as well as the non-normalized version found by solving the linear system. We will see that it is possible to find explicit formulas for the PageRank in some simple link structures and using these formulas take a more in-depth look at the behavior of the ranking as the system changes.