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We study a two states opinion formation model driven by PageRank nodeinfluence and report an extensive numerical study on how PageRank affectscollective opinion formations in large-scale empirical directed networks. Inour model the opinion of a node can be updated by the sum of its neighbornodes' opinions weighted by the node influence of the neighbor nodes at eachstep. We consider PageRank probability and its sublinear power as nodeinfluence measures and investigate evolution of opinion under variousconditions. First, we observe that all networks reach steady state opinionafter a certain relaxation time. This time scale is decreasing with theheterogeneity of node influence in the networks. Second, we find that our modelshows consensus and non-consensus behavior in steady state depending on typesof networks: Web graph, citation network of physics articles, and LiveJournalsocial network show non-consensus behavior while Wikipedia article networkshows consensus behavior. Third, we find that a more heterogeneous influencedistribution leads to a more uniform opinion state in the cases of Web graph,Wikipedia, and Livejournal. However, the opposite behavior is observed in thecitation network. Finally we identify that a small number of influential nodescan impose their own opinion on significant fraction of other nodes in allconsidered networks. Our study shows that the effects of heterogeneity of nodeinfluence on opinion formation can be significant and suggests furtherinvestigations on the interplay between node influence and collective opinionin networks.

Opinion formation driven by PageRank node influence on directed networks