PageRank model of opinion formation on social networks

TL;DR

This paper introduces a PageRank-based model for opinion formation on social networks, revealing how elite nodes influence society and how opinion dynamics depend on network structure and parameters.

Contribution

It presents a novel PageRank-based opinion formation model and analyzes its properties on real-world social networks, including the effects of elite influence and opinion bistability.

Findings

Elite nodes can significantly influence society opinion.

Bistability range depends on conformist parameter.

LiveJournal and Twitter show stronger totalitarian tendencies.

Abstract

We propose the PageRank model of opinion formation and investigate its rich properties on real directed networks of Universities of Cambridge and Oxford, LiveJournal and Twitter. In this model the opinion formation of linked electors is weighted with their PageRank probability. We find that the society elite, corresponding to the top PageRank nodes, can impose its opinion to a significant fraction of the society. However, for a homogeneous distribution of two opinions there exists a bistability range of opinions which depends on a conformist parameter characterizing the opinion formation. We find that LiveJournal and Twitter networks have a stronger tendency to a totalitar opinion formation. We also analyze the Sznajd model generalized for scale-free networks with the weighted PageRank vote of electors.