Opinion formation driven by PageRank node influence on directed networks

TL;DR

This paper investigates how PageRank-based node influence affects opinion formation in large directed networks, revealing effects on consensus, opinion distribution, and the role of influential nodes.

Contribution

It provides an extensive numerical analysis of opinion dynamics driven by PageRank influence, highlighting the impact of influence heterogeneity on collective opinions.

Findings

Networks reach steady state opinions after relaxation time.

Heterogeneity in influence affects opinion uniformity differently across networks.

A small number of influential nodes can sway large parts of the network.

Abstract

We study a two states opinion formation model driven by PageRank node influence and report an extensive numerical study on how PageRank affects collective opinion formations in large-scale empirical directed networks. In our model the opinion of a node can be updated by the sum of its neighbor nodes' opinions weighted by the node influence of the neighbor nodes at each step. We consider PageRank probability and its sublinear power as node influence measures and investigate evolution of opinion under various conditions. First, we observe that all networks reach steady state opinion after a certain relaxation time. This time scale is decreasing with the heterogeneity of node influence in the networks. Second, we find that our model shows consensus and non-consensus behavior in steady state depending on types of networks: Web graph, citation network of physics articles, and LiveJournal social network show non-consensus behavior while Wikipedia article network shows consensus behavior. Third, we find that a more heterogeneous influence distribution leads to a more uniform opinion state in the cases of Web graph, Wikipedia, and Livejournal. However, the opposite behavior is observed in the citation network. Finally we identify that a small number of influential nodes can impose their own opinion on significant fraction of other nodes in all considered networks. Our study shows that the effects of heterogeneity of node influence on opinion formation can be significant and suggests further investigations on the interplay between node influence and collective opinion in networks.