On the Localization of the Personalized PageRank of Complex Networks

TL;DR

This paper provides an analytical framework for understanding the localization of personalized PageRank in directed complex networks, including dangling nodes, and applies it to social network user classification.

Contribution

It offers a new analytical characterization of personalized PageRank values and introduces methods to identify leaders and competitors in networks based on adjacency and dangling node data.

Findings

Analytical characterization of personalized PageRank values

Theoretical justification for social network user classification model

Methods to locate leaders and competitors in complex networks

Abstract

In this paper new results on personalized PageRank are shown. We consider directed graphs that may contain dangling nodes. The main result presented gives an analytical characterization of all the possible values of the personalized PageRank for any node.We use this result to give a theoretical justification of a recent model that uses the personalized PageRank to classify users of Social Networks Sites. We introduce new concepts concerning competitivity and leadership in complex networks. We also present some theoretical techniques to locate leaders and competitors which are valid for any personalization vector and by using only information related to the adjacency matrix of the graph and the distribution of its dangling nodes.