Tipping Points of Diehards in Social Consensus on Large Random Networks

  • W. Zhang
  • C. Lim
  • B. Szymanski
Part of the Studies in Computational Intelligence book series (SCI, volume 424)


We introduce the homogeneous pair approximation to the Naming Game (NG) model, establish a six dimensional ODE for the two-word NG. Our ODE reveals how the dynamical behavior of the NG changes with respect to the average degree < k > of an uncorrelated network and shows a good agreement with the numerical results.We also extend the model to the committed agent case and show the shift of the tipping point on sparse networks.


Degree Distribution Average Degree Voter Model Social Consensus Naming Game 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Baronchelli, A., Felici, M., Loreto, V., Caglioti, E., Steels, L.: Sharp transition towards shared vocabularies in multi-agent systems. J. Stat. Mech.: Theory Exp., P06014 (2006)Google Scholar
  2. 2.
    Baronchelli, A.: Role of feedback and broadcasting in the naming game. Phys. Rev. E 83, 046103 (2011)CrossRefGoogle Scholar
  3. 3.
    Pugliese, E., Castellano, C.: Heterogeneous pair approximation for voter models on networks. Eur. Lett. 88(5), 58004 (2009)CrossRefGoogle Scholar
  4. 4.
    Chung, F., Lu, L.: The Average Distances in Random Graphs with Given Expected Degrees. Proceeding of National Academy of Science 99, 15879–15882 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Vazquez, F., Eguluz, V.M.: Analytical solution of the voter model on uncorrelated networks. New Journal of Physics 10, 063011 (2008)CrossRefGoogle Scholar
  6. 6.
    Xie, J., Sreenivasan, S., Korniss, G., Zhang, W., Lim, C., Szymanski, B.K.: Social Consensus through the Influence of Committed Minorities. Phys. Rev. E 84, 011130 (2011)CrossRefGoogle Scholar
  7. 7.
    Zhang, W., Lim, C., Sreenivasan, S., Xie, J., Szymanski, B.K., Korniss, G.: Social influencing and associated random walk models: Asymptotic consensus times on the complete graph. Chaos 21(2), 025115 (2011)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of MathematicsRensselaer Polytechnic InstituteTroyUSA

Personalised recommendations