A Coalition Formation Game Theory-Based Approach for Detecting Communities in Multi-relational Networks

  • Lihua ZhouEmail author
  • Peizhong Yang
  • Kevin Lü
  • Zidong Zhang
  • Hongmei ChenEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9098)


Community detection is a very important task in social network analysis. Most existing community detection algorithms are designed for single-relational networks. However, in the real world, social networks are mostly multi-relational. In this paper, we propose a coalition formation game theory-based approach to detect communities in multi-relational social networks. We define the multi-relational communities as the shared communities over multiple single-relational graphs, and model community detection as a coalition formation game process in which actors in a social network are modeled as rational players trying to improve group’s utilities by cooperating with other players to form coalitions. Each player is allowed to join multiple coalitions and coalitions with fewer players can merge into a larger coalition as long as the merge operation could improve the utilities of coalitions merged. We then use a greedy agglomerative manner to identify communities. Experimental results and performance studies verify the effectiveness of our approach.


Social network Community detection Coalition formation game Multi-relational network 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Francesco, F., Clara, P.: An evolutionary multiobjective approach for community discovery in dynamic networks. IEEE Transactions on Knowledge and Data Engineering 26(8), 1838–1852 (2014)CrossRefGoogle Scholar
  2. 2.
    Zhou, L., Lü, K.: Detecting communities with different sizes for social network analysis. The Computer Journal (2014). doi: 10.1093/comjnl/bxu087
  3. 3.
    Xin, Y., Yang, J., Xie, Z.Q.: A semantic overlapping community detection algorithm based on field sampling. Expert Systems with Applications 42, 366–375 (2015)CrossRefGoogle Scholar
  4. 4.
    Yuan, W., Guan, D., Lee, Y.-K., Lee, S., Hur, S.J.: Improved trust-aware recommender system using small-worldness of trust networks. Knowledge-Based Systems 23(3), 232–238 (2010)CrossRefGoogle Scholar
  5. 5.
    Wu, P., Li, S.K.: Social network analysis layout algorithm under ontology model. Journal of Software 6(7), 1321–1328 (2011)CrossRefGoogle Scholar
  6. 6.
    Wang, D., Lin, Y.-R., Bagrow, J.P.: Social networks in emergency response. In: Alhajj, R., Rokne, J. (eds.) Encyclopedia of Social Network Analysis and Mining, vol. 1, pp. 1904–1914 (2014)Google Scholar
  7. 7.
    Li, G.P., Pan, Z.S., Xiao, B., Huang, L.W.: Community discovery and importance analysis in social network. Intelligent Data Analysis 18(3), 495–510 (2014)Google Scholar
  8. 8.
    Ströele, V., Zimbrão, G., Souza, J.M.: Group and link analysis of multi-relational scientific social networks. Journal of Systems and Software 86(7), 1819–1830 (2013)CrossRefGoogle Scholar
  9. 9.
    Cai, D., Shao, Z., He, X., Yan, X., Han, J.: Community mining from multi-relational networks. In: Jorge, A.M., Torgo, L., Brazdil, P.B., Camacho, R., Gama, J. (eds.) PKDD 2005. LNCS (LNAI), vol. 3721, pp. 445–452. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  10. 10.
    Rodriguez, M., Shinavier, J.: Exposing multi-relational networks to single relational network analysis algorithms. Journal of Informetrics 4(1), 29–41 (2010)CrossRefGoogle Scholar
  11. 11.
    Szell, M., Lambiotte, R., Thurner, S.: Multirelational organization of large-scale social networks in an online world. Proceedings of the National Academy of Sciences of the United States of America 107(31), 13636–13641 (2010)CrossRefGoogle Scholar
  12. 12.
    Saad, W., Han, Z., Debbah, M., Hjørungnes, A., Basar, T.: Coalitional game theory for communication networks: a tutorial. IEEE Signal Processing Magazine 26(5), 77–97 (2009)CrossRefGoogle Scholar
  13. 13.
    Zacharias, G.L., MacMillan, J., Hemel, S.B.V. (eds.): Behavioral modeling and simulation: from individuals to societies. The National Academies Press, Washington, DC (2008)Google Scholar
  14. 14.
    Sarason, S.B.: The Psychological Sense of Community: Prospects for a Community Psychology. Jossey-Bass, San Francisco (1974)Google Scholar
  15. 15.
    Chen, W., Liu, Z., Sun, X., Wang, Y.: A Game-theoretic framework to identify overlapping communities in social networks. Data Mining and Knowledge Discovery 21(2), 224–240 (2010)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Fortunato, S.: Community detection in graphs. Physics Reports 486, 75–174 (2010)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Newman, M.E.J., Girvan, M.: Finding and evaluating community structure in networks. Physical Review E 69, 026113 (2004)CrossRefGoogle Scholar
  18. 18.
    Blondel, V.D., Guillaume, J.L., Lambiotte, R., Lefebvre, E.: Fast unfolding of communities in large networks. Journal of Statistical Mechanics: Theory and Experiment 10, P10008 (2008)CrossRefGoogle Scholar
  19. 19.
    Aynaud, T., Guillaume J.-L.: Multi-step community detection and hierarchical time segmentation in evolving networks. In: Proceedings of the fifth SNA-KDD Workshop on Social Network Mining and Analysis, in conjunction with the 17th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD 2011), San Diego, CA, pp. 21–24, August 2011Google Scholar
  20. 20.
    Wu, Z., Yin, W., Cao, J., Xu, G., Cuzzocrea, A.: Community detection in multi-relational social networks. In: Lin, X., Manolopoulos, Y., Srivastava, D., Huang, G. (eds.) WISE 2013, Part II. LNCS, vol. 8181, pp. 43–56. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  21. 21.
    Tang, L., Wang, X., Liu, H.: Community detection via heterogeneous interaction analysis. Data Mining Knowledge Discovery 25(1), 1–33 (2012)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Lin, Y.-R., Choudhury, M.D., Sundaram, H., Kelliher, A.: Discovering Multi-Relational Structure in Social Media Streams. ACM Transactions on Multimedia Computing, Communications and Applications 8(1), 1–28 (2012)CrossRefGoogle Scholar
  23. 23.
    Zhang, Z., Li, Q., Zeng, D., Gao, H.: User community discovery from multi-relational networks. Decision Support Systems 54(2), 870–879 (2013)CrossRefGoogle Scholar
  24. 24.
    Li, X.T., Ng, M.K., Ye, Y.M.: MultiComm: finding community structure in multi-dimensional networks. IEEE Transactions on Knowledge and Data Engineering 26(4), 929–941 (2014)CrossRefGoogle Scholar
  25. 25.
    Nash, J.F.: Non-cooperative games. Annals of Mathematics 54(2), 286–295 (1951)zbMATHMathSciNetCrossRefGoogle Scholar
  26. 26.
    Zlotkin, G., Rosenschein J.: Coalition cryptography and stability mechanisms for coalition formation in task oriented domains. In: Proceedings of The Twelfth National Conference on Artificial Intelligence, Seattle, Washington, August 1–4, pp. 432–437. The AAAI Press, Menlo Park (1994)Google Scholar
  27. 27.
    Alvari, H., Hashemi, S., Hamzeh, A.: Detecting overlapping communities in social networks by game theory and structural equivalence concept. In: Deng, H., Miao, D., Lei, J., Wang, F.L. (eds.) AICI 2011, Part II. LNCS, vol. 7003, pp. 620–630. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  28. 28.
    Lung, R.I., Gog, A., Chira, C.: A game theoretic approach to community detection in social networks. In: Pelta, D.A., Krasnogor, N., Dumitrescu, D., Chira, C., Lung, R. (eds.) NICSO 2011. SCI, vol. 387, pp. 121–131. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  29. 29.
    Hajibagheri, A., Alvari, H., Hamzeh, A., Hashemi, A.: Social networks community detection using the shapley value. In: 16th CSI International Symposium on Artificial Intelligence and Signal Processing (AISwww.lw20.comP), Shiraz, Iran, May 2–3, pp. 222–227 (2012)
  30. 30.
    Zhou, L., Cheng, C., Lü, K., Chen, H.: Using coalitional games to detect communities in social networks. In: Wang, J., Xiong, H., Ishikawa, Y., Xu, J., Zhou, J. (eds.) WAIM 2013. LNCS, vol. 7923, pp. 326–331. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  31. 31.
    Danon, L.: Danony, Díaz-Guilera, A., Duch, J., Arenas, A.: Comparing community structure identification. Journal of Statistical Mechanics: Theory and Experiment 9, P09008 (2005)Google Scholar
  32. 32.
    Lancichinetti, A., Fortunato, S.: Benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities. Physical Review E 80(1), 16118 (2009)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringYunnan UniversityKunmingChina
  2. 2.Brunel UniversityUxbridgeUK

Personalised recommendations