Advertisement

TTPROF: A Weighted Threshold Model for Studying Opinion Dynamics in Directed Temporal Network

  • Eeti Jain
  • Anurag Singh
  • Rajesh Sharma
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 812)

Abstract

Information flows continuously in a network of individuals, which are connected with each other as individuals tend to learn from each other through sharing of views or information. For example, an individual’s perception or ratings or reviews of a product might change with time with an effect of the opinions (representing new information) of its acquaintances. Various models have been proposed in the past to study opinion dynamics in complex settings. However, most of these models considered networks as static. In this work, we propose a directed and weighted Temporal Threshold Page Rank Opinion Formation (TTPROF) model, for studying the opinion dynamics using temporal networks. The term dynamics in this work is related to two aspects, firstly, dynamics of the network i.e., the network structure is time varying (temporal) in nature. Secondly, dynamics on the network i.e., opinions of individuals propagating on the network change with time. Opinion of every node is weighted by a factor of its page rank. A node is affected with its neighbour’s weighted opinion. A concept of threshold is added to limit the neighbours from which opinion can be shared. A parameter of the fraction of top page ranked nodes is introduced to consider the opinions of influential nodes irrespective to threshold. We simulated our model using random networks with temporal effect, which shows that as the threshold value or the fraction of top ranked nodes increases, opinions start converging faster and consensus is achieved sooner. But if any of these parameters is decreased, convergence time increases or opinions converge into multiple clusters.

Keywords

Temporal network Top ranked nodes Opinion dynamics Threshold value Page rank Timestamp 

Notes

Acknowledgements

This work is supported by H2020 framework project, SoBigData.

References

  1. 1.
    Del Vicario, M., et al.: The spreading of misinformation online. Proc. Ntl Acad. Sci. 113(3), 554–559 (2016)Google Scholar
  2. 2.
    Zollo, F., Quattrociocchi, W.: Misinformation spreading on facebook. arXiv preprint arXiv:1706.09494 (2017)
  3. 3.
    Deffuant, G., Neau, D., Frederic, A., Weisbuch, G.: Mixing beliefs among interacting agents. Adv. Complex Syst. 3(1–4), 87–98 (2000)Google Scholar
  4. 4.
    Zhang, Y.H., Liu, Q.P., Zhang, S.Y.: Opinion formation with time-varying bounded confidence. PloS One 12(3), e0172982 (2017)Google Scholar
  5. 5.
    Kandiah, V., Shepelyansky, D.L., Vivek Kandiah and: Pagerank model of opinion formation on social networks. Phys. A Statist. Mech. Appl. 391(22), 5779–5793 (2012)Google Scholar
  6. 6.
    Vazquez, F.: Opinion dynamics on coevolving networks. In: Dynamics on and of Complex Networks, Vol. 2, pp. 89–107. Springer (2013)Google Scholar
  7. 7.
    Maity, S.K., Manoj, T.V., Mukherjee, A.: Opinion formation in time-varying social networks: the case of the naming game. Phys. Rev. E 86(3), 036110 (2012)Google Scholar
  8. 8.
    Kozma, B., Barrat, A.: Consensus formation on adaptive networks. Phys. Rev. E 77(1), 016102 (2008)Google Scholar
  9. 9.
    Galton, F.: Vox populi (the wisdom of crowds). Nature 75(7), 450–451 (1907)Google Scholar
  10. 10.
    Das, A., Gollapudi, S., Munagala, K.: Modeling opinion dynamics in social networks. In: Proceedings of the 7th ACM International Conference on Web Search and Data Mining, pp. 403–412 (2014)Google Scholar
  11. 11.
    Clifford, P., Sudbury, A.: A model for spatial conflict. Biometrika 60(3), 581–588 (1973)Google Scholar
  12. 12.
    Yildiz, M.E., Pagliari, R., Ozdaglar, A., Scaglione, A.: Voting models in random networks. In: Information Theory and Applications Workshop (ITA), pp. 1–7. IEEE (2010)Google Scholar
  13. 13.
    DeGroot, M.H.: Reaching a consensus. J. Am. Statist. Assoc. 69(345), 118–121 (1974)Google Scholar
  14. 14.
    Hegselmann, R., Krause, U., et al.: Opinion dynamics and bounded confidence models, analysis, and simulation. J. Artifi. Societies Soc. Simul. 5(3) (2002)Google Scholar
  15. 15.
    Wehmuth, K., Ziviani, A., Fleury, E.: A unifying model for representing time-varying graphs. In: IEEE International Conference on Data Science and Advanced Analytics (DSAA), 2015. 36678 2015, pp. 1–10. IEEE (2015)Google Scholar
  16. 16.
    Kostakos, V.: Temporal graphs. Phys. A Statist. Mech. Appl. 388(6), 1007–1023 (2009)Google Scholar
  17. 17.
    Masuda, N., Lambiotte, R.: A guide to temporal networks. Vol. 4. World Scientific (2016)Google Scholar
  18. 18.
    Liu, C., Li, J.: Small-world and the growing properties of the chinese railway network. Front. Phys. China 2(3), 364–367 (2007)Google Scholar
  19. 19.
    Page, L., Brin, S., Motwani, R., Winograd, T.: The pagerank citation ranking: bringing order to the web. Technical Report, Stanford InfoLab (1999)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Depatment of Computer Science and EngineeringNational Institute of Technology DelhiNew DelhiIndia
  2. 2.Institute of Computer ScienceUniversity of TartuTartuEstonia

Personalised recommendations