The Naming Game in social networks: community formation and consensus engineering

  • Qiming Lu
  • G. KornissEmail author
  • Boleslaw K. Szymanski
Regular Article


We study the dynamics of the Naming Game (Baronchelli et al. in J Stat Mech Theory Exp P06014, 2006b) in empirical social networks. This stylized agent-based model captures essential features of agreement dynamics in a network of autonomous agents, corresponding to the development of shared classification schemes in a network of artificial agents or opinion spreading and social dynamics in social networks. Our study focuses on the impact that communities in the underlying social graphs have on the outcome of the agreement process. We find that networks with strong community structure hinder the system from reaching global agreement; the evolution of the Naming Game in these networks maintains clusters of coexisting opinions indefinitely. Further, we investigate agent-based network strategies to facilitate convergence to global consensus.


Naming Game Social Graph Global Agreement Global Consensus Random Geometric Graph 
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.

Supplementary material

11403_2009_57_MOESM1_ESM.pdf (201 kb)
ESM 1 (PDF 201 KB)


  1. Anghel M, Toroczkai Z, Bassler K, Korniss G (2004) Competition-driven network dynamics: emergence of a scale-free leadership structure and collective efficiency. Phys Rev Lett 92:058701 (4 pp)Google Scholar
  2. Antal T, Krapivsky P, Redner S (2005) Dynamics of social balance on networks. Phys Rev E 72: 036121CrossRefGoogle Scholar
  3. Axelrod R (1997) The dissemination of culture: a model with local convergence and global polarization. J Confl Resolut 41: 203–226CrossRefGoogle Scholar
  4. Baronchelli A, Dall’Asta L, Barrat A, Loreto V (2005) Strategies for fast convergence in semiotic dynamics. arXiv:physics/0511201Google Scholar
  5. Baronchelli A, Dall’Asta L, Barrat A, Loreto V (2006a) Topology induced coarsening in language games. Phys Rev E 73:015102(R)Google Scholar
  6. Baronchelli A, Felici M, Caglioti E, Loreto V, Steels L (2006b) Sharp transition towards shared vocabularies in multi-agent systems. J Stat Mech Theory Exp P06014Google Scholar
  7. Baronchelli A, Loreto V, Dall’Asta L, Barrat A (2006c) Bootstraping communications in language games: strategy, topology, and all that. In: Cangelosi A, Smith ADM, Smith K (eds) Proceedings of the 6th international conference on the evolution of language, World Scientific, Singapore, pp 11–18Google Scholar
  8. Ben-Naim E (2005) Opinion dynamics: rise and fall of political parties. Europhys Lett 69: 671–677CrossRefGoogle Scholar
  9. Benczik I, Benczik S, Schmitmann B, Zia R (2008) Lack of consensus in social systems. Europhys Lett 82: 48006CrossRefGoogle Scholar
  10. Blatt M, Wiseman S, Domany E (1996) Superparamagnetic clustering of data. Phys Rev Lett 76: 3251–3254CrossRefGoogle Scholar
  11. Bray A (1994) Theory of phase-ordering kinetics. Adv Phys 43: 357–459CrossRefGoogle Scholar
  12. Candia J, Mazzitello KI (2008) Mass media influence spreading in social networks with community structure. J Stat Mech Theory Exp P07007Google Scholar
  13. Castellano C, Loreto V, Barrat A, Cecconi F, Parisi D (2005) Comparison of voter and Glauber ordering dynamics on networks. Phys Rev E 71: 066107CrossRefGoogle Scholar
  14. Castellano C, Fortunato S, Loreto V (2008) Statistical physics of social dynamics. arXiv:07103256v1Google Scholar
  15. Cattuto C, Loreto V, Pietronero L (2006) Semiotic dynamics and collaborative tagging. Proc Natl Acad Sci USA 104: 1461–1464CrossRefGoogle Scholar
  16. Cattuto C, Baldassarri A, Servedio VDP, Loreto V (2007) Vocabulary growth in collaborative tagging systems. arXiv:07043316v1Google Scholar
  17. Challet D, Marsili M, Zhang YC (2005) Minority games: interacting agents in financial markets. Oxford University Press, New YorkGoogle Scholar
  18. Dall J, Christemsen M (2002) Random geometric graphs. Phys Rev E 66: 016121CrossRefGoogle Scholar
  19. Dall’Asta L, Baronchelli A, Barrat A, Loreto V (2006a) Agreement dynamics on small-world networks. Europhys Lett 73: 969–975CrossRefGoogle Scholar
  20. Dall’Asta L, Baronchelli A, Barrat A, Loreto V (2006b) Nonequilibrium dynamics of language games on complex networks. Phys Rev E 74: 036105CrossRefGoogle Scholar
  21. Deffuant G, Neau D, Amblard F, Weisbuch G (2000) Mixing beliefs among interacting agents. Adv Complex Syst 3: 87–98CrossRefGoogle Scholar
  22. Durlauf SN (1999) How can statistical mechanics contribute to social science?. Proc Natl Acad Sci USA 96: 10582–10584CrossRefGoogle Scholar
  23. Epstein JM, Axtell R (1996) Growing artificial societies: social science from the bottom up. MIT Press, CambridgeGoogle Scholar
  24. Fortunato S, Barthelemy M (2007) Resolution limit in community detection. Proc Natl Acad Sci USA 104: 36–41CrossRefGoogle Scholar
  25. Girvan M, Newman MEJ (2002) Community structure in social and biological networks. Proc Natl Acad Sci USA 99: 7821–7826CrossRefGoogle Scholar
  26. Golder S, Huberman BA (2006) Usage patterns of collaborative tagging systems. J Inf Sci 32: 198–208CrossRefGoogle Scholar
  27. Gonzáles MC, Herrmann HJ, Kertész J, Vicsek T (2007) Community structure and ethnic preferences in school friendship networks. Phys A 379: 307–316CrossRefGoogle Scholar
  28. Hegselmann R, Krause U (2002) Opinion dynamics and bounded confidence: models, analysis, and simulation. J Artif Soc Soc Simul 5: 2Google Scholar
  29. Jung WS, Moon HT, Stanley HE (2008) Dynamics of clusterd opinions in complex networks. J Econ Interact Coord 3: 81–88CrossRefGoogle Scholar
  30. Kozma B, Barrat A (2008a) Consensus formation on adaptive networks. Phys Rev E 77: 016102CrossRefGoogle Scholar
  31. Kozma B, Barrat A (2008b) Who’s talking first? Consensus or lack thereof in coevolving opinion formation models. Phys Rev Lett 100: 158701CrossRefGoogle Scholar
  32. Krapivsky PL, Redner S (2003) Dynamics of majority rule in two-state interacting spin systems. Phys Rev Lett 90:238701 (4 pp)Google Scholar
  33. Kumpula JM, Saramaki J, Kaski K, Kertész J (2007) Limited resolution in complex network community detection with Potts model approach. Eur Phys J B 56: 41–45CrossRefGoogle Scholar
  34. Lambiotte R, Ausloos M (2007) Coexistence of opposite opinions in a network with communities. J Stat Mech Theory Exp P08026Google Scholar
  35. Lim M, Metzler R, Bar-Yam Y (2007) Global pattern formation and ethnic/cultural violence. Science 317: 1540–1544CrossRefGoogle Scholar
  36. Lin BY, Ren J, Yang HJ, Wang BH (2006) Naming Game on smal-world networks: the role of clustering structure. arXiv:physics/0607001Google Scholar
  37. Lorenz J (2007) Continuous opinion dynamics under bounded confidence: a survey. Int J Mod Phys C 18: 1819–1838CrossRefGoogle Scholar
  38. Lorenz J (2008) Fostering consensus in multidimensional continuous opinion dynamics under bounded confidence. In: Helbing D (ed) Managing complexity: insights, concepts, applications. Springer Series in Understanding Complex Systems, pp 321–334Google Scholar
  39. Lu Q, Korniss G, Szymanski BK (2006) Naming Games in spatially-embeded random networks. In: Proceedings of the 2006 American association for artificial intelligence fall symposium series, interaction and emergent phenomena in societies of agents. AAAI Press, Menlo Park, pp 148–155Google Scholar
  40. Lu Q, Korniss G, Szymanski BK (2008) Naming games in two-dimensional and small-world-connected random geometric networks. Phys Rev E 77: 016111CrossRefGoogle Scholar
  41. Mazzitello KI, Candia J, Dossetti V (2007) Effects of mass media and dultural drift in a model for social influence. Int J Mod Phys 18: 1475–1482CrossRefGoogle Scholar
  42. McConchie A (2002) The great pop vs. soda controversy.
  43. Meester R, Roy R (1996) Continuum percolation. Cambridge University Press, CambridgeGoogle Scholar
  44. Moody J (2001) Race, school integration and friendship segragation in America. Am J Sociol 107: 679–716CrossRefGoogle Scholar
  45. Newman MEJ (2004) Detecting community structure in networks. Eur Phys J B 38: 321–330CrossRefGoogle Scholar
  46. Newman MEJ (2006) Finding community structure in networks using the eigenvectors of matrices. Phys Rev E 74: 036104CrossRefGoogle Scholar
  47. Newman MEJ, Girvan M (2004) Finding and evaluating community structure in networks. Phys Rev E 69: 026113CrossRefGoogle Scholar
  48. Onnela JP, Saramaki J, Hyvonen J, Szabó G, Lazer D, Kaski K, Kertész J, Barabási AL (2007) Structure and tie strength in mobile commnication networks. Proc Natl Acad Sci USA 104: 7332–7336CrossRefGoogle Scholar
  49. Palla G, Derényi I, Farkas I, Vicsek T (2005) Uncovering the overlapping community structure of complex networks in nature and society. Nature 435: 814–818CrossRefGoogle Scholar
  50. Palla G, Barabási AL, Vicsek T (2007) Quantifying social group evolution. Nature 446: 664–667CrossRefGoogle Scholar
  51. Penrose M (2003) Random geometric graphs. Oxford University Press, OxfordCrossRefGoogle Scholar
  52. Reichardt J, Bornholdt S (2004) Detecting fuzzy community structures in complex networks with a Potts model. Phys Rev Lett 93: 218701CrossRefGoogle Scholar
  53. San Miguel M, Eguiluz VM, Toral R, Klemm K (2005) Binary and multivariate stochastic models of consensus formation. Comput Sci Eng 7(6): 67–73CrossRefGoogle Scholar
  54. Schelling TC (1971) Dynamic models of segregation. J Math Sociol 1: 143–186Google Scholar
  55. Scott J (2000) Social network analysis: a handbook. 2nd edn. Sage, LondonGoogle Scholar
  56. Sood V, Redner S (2005) Voter model on heterogeneous graphs. Phys Rev Lett 94: 178–701CrossRefGoogle Scholar
  57. Sznajd-Weron K, Sznajd J (2000) Opinion evolution in closed community. Int J Mod Phys C 11: 1157–1165CrossRefGoogle Scholar
  58. Vinkovic D, Kirman A (2006) A physical analogue of the Schelling model. Proc Natl Acad Sci USA 19: 19261–19265CrossRefGoogle Scholar
  59. Wang WX, Lin BY, Tang CL, Chen GR (2007) Agreement dynamics of finite-memory language games on networks. Eur Phys J B 60: 529–536CrossRefGoogle Scholar
  60. Watts DJ, Strogatz SH (1998) Collective dynamics of small-world networks. Nature 393: 440–442CrossRefGoogle Scholar
  61. Wu F, Huberman BA (2004) Finding communities in linear time: a physics approach. Eur Phys J B 38: 331–338CrossRefGoogle Scholar
  62. Zhang J (2004) A dynamic model of residential segregation. J Math Sociol 28: 147–170CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of Physics, Applied Physics and AstronomyRensselaer Polytechnic InstituteTroyUSA
  2. 2.Department of Computer Science, Center for Pervasive Computing and NetworkingRensselaer Polytechnic InstituteTroyUSA

Personalised recommendations