Power Indices of Influence Games and New Centrality Measures for Agent Societies and Social Networks

  • Xavier Molinero
  • Fabián Riquelme
  • Maria Serna
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 291)


We propose as centrality measures for social networks two classical power indices, Banzhaf and Shapley-Shubik, and two new measures, effort and satisfaction, related to the spread of influence process that emerge from the subjacent influence game. We perform a comparison of these measures with three well known centrality measures, degree, closeness and betweenness, applied to three simple social networks.


Social Network Centrality Power index Influence game Simple game 


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  1. 1.
    Aziz, H.: Algorithmic and complexity aspects of simple coalitional games. PhD Thesis, Department of Computer Science, University of Warwick (2009)Google Scholar
  2. 2.
    de Nooy, W., Mrvar, A., Batagelj, V.: Exploratory social network analysis with Pajek. Structural analysis in the social sciences, vol. 27. Cambridge Univ. Press (2005)Google Scholar
  3. 3.
    Everett, M.G., Borgatti, S.P.: The centrality of groups and classes. Journal of Mathematical Sociology 23(3), 181–201 (1999)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Freeman, L.C.: Centrality in social networks: Conceptual clarification. Social Networks 1(3), 215–239 (1979)CrossRefGoogle Scholar
  5. 5.
    Freixas, J.: Power indices. In: Cochran, J.J., Cox, L.A., Keskinocak, P., Kharoufeh, J.P., Smith, J.C. (eds.) Wiley Encyclopedia of Operations Research and Management Science, vol. 8, John Wiley & Sons (2011)Google Scholar
  6. 6.
    Hlebec, V.: Recall versus recognition: Comparison of two alternative procedures for collecting social network data. In: Ferligoj, A., Kramberger, T. (eds.) Proceedings of the International Conference on Methodology and Statistics, pp. 121–128 (1992, 1993)Google Scholar
  7. 7.
    Kempe, D., Kleinberg, J., Tardos, É.: Maximizing the spread of influence through a social network. In: Getoor, L., Senator, T.E., Domingos, P., Faloutsos, C. (eds.) Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 137–146 (2003)Google Scholar
  8. 8.
    Latora, V., Marchiori, M.: A measure of centrality based on network efficiency. New Journal of Physics 9(6) (2007)Google Scholar
  9. 9.
    Michalak, T.P., Aadithya, K.V., Szczepański, P.L., Ravindran, B., Jennings, N.R.: Efficient computation of the Shapley value for game-theoretic network centrality. Journal of Artificial Intelligence Research 46, 607–650 (2013)zbMATHMathSciNetGoogle Scholar
  10. 10.
    Molinero, X., Riquelme, F., Serna, M.J.: Social influence as a voting system: A complexity analysis of parameters and properties. CoRR, abs/1208.3751v3 (2014)Google Scholar
  11. 11.
    Moreno, J.L.: The sociometry reader. Free Press (1960)Google Scholar
  12. 12.
    Sun, J., Tang, J.: A survey of models and algorithms for social influence analysis. In: Aggarwal (ed.) Social Network Data Analytics, pp. 177–214 (2011)Google Scholar
  13. 13.
    Taylor, A., Zwicker, W.: Simple games: Desirability relations, trading, pseudoweightings. Princeton University Press (1999)Google Scholar
  14. 14.
    van den Brink, R., Rusinowska, A., Steffen, F.: Measuring power and satisfaction in societies with opinion leaders: dictator and opinion leader properties. Homo Oeconomicus 28(1-2), 161–185 (2011)Google Scholar
  15. 15.
    Wasserman, S., Faust, K.: Social network analysis: Methods and applications. Structural analysis in the social sciences, vol. 8. Cambridge Univ. Press (1994)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Xavier Molinero
    • 1
  • Fabián Riquelme
    • 2
  • Maria Serna
    • 2
  1. 1.Dept. of Applied Mathematics IIIUPCManresaSpain
  2. 2.Dept. de Llenguatges i Sistemes InformàticsUPCBarcelonaSpain

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