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Opinion formation driven by PageRank node influence on directed networks

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  • Eom, Young-Ho
  • Shepelyansky, Dima L.

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.

Suggested Citation

  • Eom, Young-Ho & Shepelyansky, Dima L., 2015. "Opinion formation driven by PageRank node influence on directed networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 707-715.
    • Handle: RePEc:eee:phsmap:v:436:y:2015:i:c:p:707-715
    DOI: 10.1016/j.physa.2015.05.095
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    Citations

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    Cited by:

    1. Ma, Ning & Liu, Yijun & Chi, Yuxue, 2018. "Influencer discovery algorithm in a multi-relational network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 415-425.
    2. Wang, Qiyao & Jin, Yuehui & Cheng, Shiduan & Yang, Tan, 2017. "ConformRank: A conformity-based rank for finding top-k influential users," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 474(C), pages 39-48.
    3. Célestin Coquidé & José Lages & Dima Shepelyansky, 2024. "Opinion Formation in the World Trade Network," Post-Print hal-04461784, HAL.
    4. C'elestin Coquid'e & Jos'e Lages & Dima L. Shepelyansky, 2023. "Prospects of BRICS currency dominance in international trade," Papers 2305.00585, arXiv.org.

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