Fixed points of Personalized PageRank centrality: From irreducible to reducible networks

TL;DR

This paper characterizes the existence and uniqueness of fixed points in Personalized PageRank for complex networks, relating them to the network's strongly connected components and using a feedback approach with Perron vectors.

Contribution

It provides a complete characterization of fixed points of Personalized PageRank in reducible and irreducible networks, introducing a feedback method for exact computation.

Findings

Fixed points depend on the network's strongly connected components.

A feedback-PageRank method computes fixed points using Perron vectors.

The analysis covers both reducible and irreducible network cases.

Abstract

In this paper we analyze the PageRank of a complex network as a function of its personalization vector. By using this approach, a complete characterization of the existence and uniqueness of fixed points of PageRank of a graph is given in terms of the number and nature of its strongly connected components. The method presented includes the use of a feedback-PageRank in order to compute exactly the fixed points following the classic Power's Method in terms of the (left-hand) Perron vector of each strongly connected components.