Silhouette for the Evaluation of Community Structures in Multiplex Networks

Conference paper
Part of the Springer Proceedings in Complexity book series (SPCOM)

Abstract

This paper focuses on the silhouette as validity criterion for community structures in networks, with emphasis on multiplex networks. We propose a versatile definition of the silhouette, by generalizing it to encompass different scenarios of proximity between entities in a network, where the distance notion can be geodesic-based or homophily-oriented. To the best of our knowledge, we are the first to propose this twofold perspective on the silhouette and its extension to deal with multiplex networks. We also define an approximate variant of the multiplex silhouette to speed up its computation on large networks, based on the exploitation of central nodes to be regarded as community representatives. Experimental results performed on benchmark real-world network datasets have revealed that the proposed multiplex silhouette is positively correlated with its approximate version, while the latter proved to be much faster in terms of execution time.

References

  1. 1.
    Aldecoa, R., Marín, I.: Surprise maximization reveals the community structure of complex networks. Sci. Rep. 3 (2013)Google Scholar
  2. 2.
    Amelio, A., Tagarelli, A.: Revisiting resolution and inter-layer coupling factors in modularity for multilayer networks. In: Proceedings of the IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM). pp. 266–273 (2017)Google Scholar
  3. 3.
    Berlingerio, M., Coscia, M., Giannotti, F.: Finding and characterizing communities in multidimensional networks. In: Proceedings of the ASONAM. pp. 490–494 (2011)Google Scholar
  4. 4.
    Bródka, P., Kazienko, P.a., Koł oszczyk, B.: Predicting group evolution in the social network. In: Proceedings of the International Conference on Social Informatics (SocInfo). pp. 54–67 (2012)Google Scholar
  5. 5.
    Chakraborty, T., Dalmia, A., Mukherjee, A., Ganguly, N.: Metrics for Community Analysis: A Survey. arXiv:1604.03512 (2016)
  6. 6.
    Chakraborty, T., Srinivasan, S., Ganguly, N., Mukherjee, A., Bhowmick, S.: On the permanence of vertices in network communities. In: Proceedings of the ACM Conference on Knowledge Discovery and Data Mining (KDD). pp. 1396–1405 (2014)Google Scholar
  7. 7.
    Creusefond, J., Largillier, T., Peyronnet, S.: Finding compact communities in large graphs. In: Proceedings of the ASONAM. pp. 1457–1464 (2015)Google Scholar
  8. 8.
    Creusefond, J., Largillier, T., Peyronnet, S.: On the evaluation potential of quality functions in community detection for different contexts. In: Proceedings of the International Conference and School on Advances in Network Science (NetSci-X). pp. 111–125 (2016)Google Scholar
  9. 9.
    De Domenico, M., Lancichinetti, A., Arenas, A., Rosvall, M.: Identifying modular flows on multilayer networks reveals highly overlapping organization in interconnected systems. Phys. Rev. X 5, 011027 (2015)Google Scholar
  10. 10.
    De Domenico, M., Nicosia, V., Arenas, A., Latora, V.: Structural reducibility of multilayer networks. Nat. Commun. 6, 6864 (2015)CrossRefGoogle Scholar
  11. 11.
    Dickison, M.E., Magnani, M., Rossi, L.: Multilayer Social Networks. Cambridge University Press, UK (2016)CrossRefGoogle Scholar
  12. 12.
    Estrada, E.: Community detection based on network communicability. Chaos 21 (2011)Google Scholar
  13. 13.
    Gustafsson, M., Hornquist, M., Lombardi, A.: Comparison and validation of community structures in complex networks. Physica A 367, 559–576 (2006)ADSCrossRefGoogle Scholar
  14. 14.
    Kim, J., Lee, J.: Community detection in multi-layer graphs: a survey. SIGMOD Rec. 44(3), 37–48 (2015)CrossRefGoogle Scholar
  15. 15.
    Mucha, P.J., Richardson, T., Macon, K., Porter, M.A., Onnela, J.P.: Community structure in time-dependent, multiscale, and multiplex networks. Science 328(5980), 876–878 (2010)ADSMathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Newman, M.E.J., Girvan, M.: Finding and evaluating community structure in networks. Phys. Rev. E 69, 026113 (2004)ADSCrossRefGoogle Scholar
  17. 17.
    Nicosia, V., Mangioni, G., Carchiolo, V., Malgeri, M.: Extending the definition of modularity to directed graphs with overlapping communities. J. Stat. Mech. Theory Exper. (03), P03024 (2009)Google Scholar
  18. 18.
    Rousseeuw, P.J.: Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. J. Comput. Appl. Math. 20, 53–65 (1987)CrossRefMATHGoogle Scholar
  19. 19.
    Tagarelli, A., Amelio, A., Gullo, F.: Ensemble-based community detection in multilayer networks. Data Min. Knowl. Discov. 31(5), 1506–1543 (2017)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Tang, L., Wang, X., Liu, H.: Uncoverning groups via heterogeneous interaction analysis. In: Proceeding of the IEEE International Conference on Data Mining (ICDM). pp. 503–512 (2009)Google Scholar
  21. 21.
    Traag, V.A., Krings, G., Dooren, P.V.: Significant scales in community structure. Sci. Rep. 3 (2013)Google Scholar
  22. 22.
    Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393(6684), 409–10 (1998)CrossRefMATHGoogle Scholar
  23. 23.
    Yang, J., Leskovec, J.: Defining and evaluating network communities based on ground-truth. In: Proceedings of the IEEE International Conference on Data Mining (ICDM) (2012)Google Scholar
  24. 24.
    Zhang, H., Wang, C., Lai, J., Yu, P.S.: Modularity in Complex Multilayer Networks with Multiple Aspects: A Static Perspective. CoRR (2016). arXiv:abs/1605.06190

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.DIMES, University of CalabriaRende (CS)Italy

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