Exploring the Map Equation: Community Structure Detection in Unweighted, Undirected Networks

  • Rodica Ioana LungEmail author
  • Mihai-Alexandru Suciu
  • Noémi Gaskó
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 837)


The map equation is one of the most efficient methods of evaluating a possible community structure of a network, computed by using Shanon’s entropy and probabilities that a random walker would exit a community or would wonder inside it. Infomap, the method that optimizes the map equation to reveal community structures, is one of the most efficient computational approach to this problem when dealing with weighted, directed or hierarchical networks. However, for some unweighted and undirected networks, Infomap fails completely to uncover any structure. In this paper we propose an alternate way of computing probabilities used by the map equation by adding information about 3-cliques corresponding to links in order to enhance the behavior of Infomap in unweighted networks. Numerical experiments performed on standard benchmarks show the potential of the approach.


Community structure Social networks Unweighted graphs Infomap 



This work was supported by a grant of the Romanian National Authority for Scientific Research and Innovation, CNCS - UEFISCDI, project number PN-II-RU-TE-2014-4-2332.


  1. 1.
    Cormen, T.H., Stein, C., Rivest, R.L., Leiserson, C.E.: Introduction to Algorithms, 2nd edn. McGraw-Hill Higher Education, New York City (2001)zbMATHGoogle Scholar
  2. 2.
    Fortunato, S.: Community detection in graphs. Phys. Rep. 486, 75–174 (2010). Scholar
  3. 3.
    Girvan, M., Newman, M.E.J.: Community structure in social and biological networks. Proc. Nat. Acad. Sci. 99(12), 7821–7826 (2002). Scholar
  4. 4.
    Gong, M., Ma, L., Zhang, Q., Jiao, L.: Community detection in networks by using multiobjective evolutionary algorithm with decomposition. Phys. A: Stat. Mech. Appl. 391(15), 4050–4060 (2012). Scholar
  5. 5.
    Lancichinetti, A., Fortunato, S.: Benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities. Phys. Rev. E 80, 016118 (2009). Scholar
  6. 6.
    Lancichinetti, A., Fortunato, S., Kertész, J.: Detecting the overlapping and hierarchical community structure in complex networks. New J. Phys. 11(3), 033015 (2009)CrossRefGoogle Scholar
  7. 7.
    Lancichinetti, A., Radicchi, F., Ramasco, J.J., Fortunato, S.: Finding statistically significant communities in networks. PloS One 6(4), e18961 (2011)CrossRefGoogle Scholar
  8. 8.
    Lung, R., Suciu, M., Gasko, N.: Noisy extremal optimization. Soft Comput. 1–18 (2015).
  9. 9.
    Lusseau, D., Schneider, K., Boisseau, O., Haase, P., Slooten, E., Dawson, S.: The bottlenose dolphin community of doubtful sound features a large proportion of long-lasting associations. Behav. Ecol. Sociobiol. 54(4), 396–405 (2003). Scholar
  10. 10.
    Rosvall, M., Bergstrom, C.T.: Maps of random walks on complex networks reveal community structure. Proc. Nat. Acad. Sci. 105(4), 1118–1123 (2008). Scholar
  11. 11.
    Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27(3), 379–423 (1948). Scholar
  12. 12.
    Zachary, W.W.: An information flow model for conflict and fission in small groups. J. Anthropol. Res. 33(4), 452–473 (1977)CrossRefGoogle Scholar
  13. 13.
    Zhang, Z.Y., Sun, K.D., Wang, S.Q.: Enhanced community structure detection in complex networks with partial background information. Sci. Rep. 3, 3241 (2013). Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Rodica Ioana Lung
    • 1
    Email author
  • Mihai-Alexandru Suciu
    • 1
  • Noémi Gaskó
    • 1
  1. 1.Center for the Study of ComplexityBabeş-Bolyai UniversityCluj-NapocaRomania

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