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

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.