Banzhaf Index for Influence Maximization

  • Balaji Vasan SrinivasanEmail author
  • Arava Sai Kumar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9471)


Social media has changed the way people communicate with each other and has brought people together. Enterprises are increasingly using it as a medium for marketing activities. However, due to the size of these networks, marketers often look for key customers (influencers) to drive the campaign to the community. In this paper, we take a game theoretic approach to identify key influencers in a network. We begin with defining coalition games to model the social network and then use the concept of Banzhaf index to measure the utility of each user to the coalition. We further extend this concept towards identification of influencers and compare the resulting algorithm against existing works on influence maximization on several datasets. Improvements are observed.


Social Network Centrality Measure Collaboration Network Marginal Contribution Coalition 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.
    Aadithya, K.V., Ravindran, B., Michalak, T.P., Jennings, N.R.: Efficient computation of the shapley value for centrality in networks. In: Saberi, A. (ed.) WINE 2010. LNCS, vol. 6484, pp. 1–13. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  2. 2.
    Banzhaf, J.F.: Weighted voting doesn’t work: a mathematical analysis. Rutgers Law Review 19, 317–343 (1965)Google Scholar
  3. 3.
    Chen, W., Wang, C., Wang, Y.: Scalable influence maximization for prevalent viral marketing in large-scale social networks. In: Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining, pp. 1029–1038. ACM (2010)Google Scholar
  4. 4.
    Chen, W., Wang, Y., Yang, S.: Efficient influence maximization in social networks. KDD (2009)Google Scholar
  5. 5.
    Domingos, P., Richardson, M.: Mining the network value of customers. In: Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining, pp. 57–66. ACM (2001)Google Scholar
  6. 6.
    Everett, M.G., Borgatti, S.: The centrality of groups and classes. Journal of Mathematical Sociology 23(3), 181–201 (1999)CrossRefzbMATHGoogle Scholar
  7. 7.
    Fatima, S.S., Wooldridge, M., Jennings, N.: A randomized method for the shapley value for the voting game. In: Proceedings of the 11th International Joint Conference on Autonomous Agents and Multi-Agent Systems, pp. 955–92. AAMAS (2007)Google Scholar
  8. 8.
    Granovetter, M.: Threshold models of collective behavior. American Journal of Sociology 83(6), 1420–1443 (1978)CrossRefGoogle Scholar
  9. 9.
    Grofman, B., Owen, G.: A game theoretic approach to measuring centrality in social networks. Social Networks 4, 213–224 (1982)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Kempe, D., Kleinberg, J., Tardos, É.: Maximizing the spread of influence through a social network. In: Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining, pp, 137–146. ACM (2003)Google Scholar
  11. 11.
    Leskovec, J., Krause, A., Guestrin, C., Faloutsos, C., VanBriesen, J., Glance, N.: Cost-effective outbreak detection in networks. In: Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining, pp. 420–429. ACM (2007)Google Scholar
  12. 12.
    Matsui, Y., Matsui, T.: Np-completeness for calculating power indices of weighted majority games. Theoretical Computer Science 263(1–2), 305–310 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Narayanam, R., Narahari, Y.: A shapley value-based approach to discover influential nodes in social networks. IEEE Transactions on Automation Science and Engineering 99, 1–18 (2010)Google Scholar
  14. 14.
    Young, H.P.: The diffusion of innovations in social networks. In: Proceedings volume in the Santa Fe Institute studies in the sciences of complexity Santa Fe Institute Studies on the Sciences of Complexity, vol. 3, pp. 267–282. Oxford University Press, US (2006)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Adobe Research Big Data Intelligence LabsBangaloreIndia
  2. 2.Adobe Systems India Private LimitedBangaloreIndia

Personalised recommendations