PageRank for evolving link structures
This work provides incremental insights into PageRank dynamics for evolving networks, relevant for search engine optimization and network analysis.
The paper analyzes the PageRank algorithm's behavior in dynamically evolving link structures, such as lines and complete graphs, and derives explicit formulas for PageRank in these simple cases to examine ranking changes as nodes or links are added or removed.
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.