Can the PageRank centrality be manipulated to obtain any desired ranking?

TL;DR

This paper investigates the controllability of PageRank rankings, revealing how they can be manipulated through structural and parametric changes, and compares different centrality measures on various network datasets.

Contribution

It introduces a geometric approach to analyze PageRank controllability and applies it to biplex PageRank, providing new insights into ranking manipulation and centrality measure comparison.

Findings

PageRank outcomes can be systematically controlled and manipulated.

A geometric characterization of PageRank rankings is proposed.

Numerical comparisons of centrality measures on real and synthetic networks are conducted.

Abstract

The significance of the PageRank algorithm in shaping the modern Internet cannot be overstated, and its Complex Network theory foundations continue to be a subject of research. In this article we carry out a systematic study of the structural and parametric controllability of PageRank's outcomes, translating a spectral Graph Theory problem into a geometric one, where a natural characterization of its rankings emerges. Furthermore, we show that the change of perspective employed can be applied to the biplex PageRank proposal, performing numerical computations on both real and synthetic network datasets to compare centrality measures used.