Detecting Overlapping Communities with Triangle-Based Rough Local Expansion Method

  • Zehua ZhangEmail author
  • Nan Zhang
  • Caiming Zhong
  • Litian Duan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9436)


Overlapping communities structures could effectively reveal the internal relationships in real networks, especially on the ownership problems on the nodes in overlapping areas between communities. Hence, the overlapping community detection research becomes a hotspot topic on graph mining in the decade, while the local expansion methods based on structural fitness function could simultaneously discover overlapped and hierarchical structures. Aimed at community drift and redundant calculation problems on general local expansion methods, the paper presents a novel local expansion method based on rough neighborhood that carries out the heuristic technology by the community seed inspiration and the triangle optimization on the boundary domain. The method could directly generate natural overlaps between communities, reduce the computational complexity and improve the detection on the overlapped boundary area. Finally, the experimental results on some real networks also show that the rough expansion method based on triangle optimization could be more effective in detecting the overlapping structures.


Rough set theory Overlapping community detection Rough neighborhood expansion Triangle optimization 



The research is supported by the Creative Research Groups and the Qualified Personnel Foundation of Taiyuan University of Technology of China (Grant No. 2014TD056), the National Natural Science Foundation of China (No. 61503273 and 61403329) and General Program (No. 61175054), and the Natural Science Foundation of Shandong Province (No. ZR2013FQ020).


  1. 1.
    Girvan, M., Newman, M.E.J.: Community structure in social and biological networks. Proc. Natl. Acad. Sci. 99(12), 7821–7826 (2002)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Fortunato, S.: Community detection in graphs. Phys. Rep. 486(3), 75–174 (2010)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Clauset, A.: Finding local community structure in networks. Phys. Rev. E 72(2), 026132 (2005)CrossRefGoogle Scholar
  4. 4.
    Dernyi, I., Palla, G., Vicsek, T.: Clique percolation in random networks. Phys. Rev. Lett. 94(16), 160202 (2005)CrossRefGoogle Scholar
  5. 5.
    Evans, T.S., Lambiotte, R.: Line graphs, link partitions, and overlapping communities. Phys. Rev. E 80(1), 016105 (2009)CrossRefGoogle Scholar
  6. 6.
    Lancichinetti, A., Fortunato, S.: Detecting the overlapping and hierarchical community structure in complex networks. New J. Phys. 11(3), 033015 (2009)CrossRefGoogle Scholar
  7. 7.
    Ahn, Y.Y., Bagrow, J.P., Lehmann, S.: Link communities reveal multiscale complexity in networks. Nature 466(7307), 761–764 (2010)CrossRefGoogle Scholar
  8. 8.
    Ball, B., Karrer, B., Newman, M.E.J.: An efficient and principled method for detecting communities in networks. Phys. Rev. E 84(3), 036103 (2011)CrossRefGoogle Scholar
  9. 9.
    Havemann, F., Heinz, M., Struck, A., et al.: Identification of overlapping communities and their hierarchy by locally calculating community-changing resolution levels. J. Stat. Mech. Theory Experiment 2011(01), P01023 (2011)CrossRefGoogle Scholar
  10. 10.
    Yang, J., Leskovec, J.: Defining and evaluating network communities based on ground-truth. Knowl. Inf. Syst. 42(1), 181–213 (2015)CrossRefGoogle Scholar
  11. 11.
    Gregory, S.: Fuzzy overlapping communities in networks. J. Stat. Mech. Theory Experiment 2011(02), P02017 (2011)CrossRefGoogle Scholar
  12. 12.
    Zhang, Z., Miao, D., Qian, J.: Detecting overlapping communities with heuristic expansion method based on rough neighborhood. Chin. J. Comput. 36(10), 2078–2086 (2013)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Pawlak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 11(5), 341–356 (1982)CrossRefGoogle Scholar
  14. 14.
    Yao, Y.Y.: Relational interpretations of neighborhood operators and rough set approximation operators. Inf. Sci. 111(1), 239–259 (1998)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Hu, Q., Yu, D., Liu, J., et al.: Neighborhood rough set based heterogeneous feature subset selection. Inf. Sci. 178(18), 3577–3594 (2008)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Radicchi, F., Castellano, C., Cecconi, F., Loreto, V., Parisi, D.: Defining and identifying communities in networks. Proc. Natl. Acad. Sci. 101, 2658–2663 (2004)CrossRefGoogle Scholar
  17. 17.
    Wu, W., Zhang, W.: Neighborhood operator systems and approximations. Inf. Sci. 144(1), 201–217 (2002)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Lin, G., Qian, Y., Li, J.: NMGRS: neighborhood-based multigranulation rough sets. Int. J. Approximate Reasoning 53, 1080–1093 (2012)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Lusseau, D.: The emergent properties of a dolphin social network. Proc. R. Soc. Lond. Ser. B Biol. Sci. 270, S186–S188 (2003)CrossRefGoogle Scholar
  20. 20.
    Newman, M.E.J.: Finding community structure in networks using the eigenvectors of matrices. Phys. Rev. E 74(3), 036104 (2006)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Lee, C., Reid, F., McDaid, A., et al.: Detecting highly overlapping community structure by greedy clique expansion. In: Proceedings of the 4th SNA-KDD Workshop, pp. 33–42 (2010)Google Scholar
  22. 22.
    Lin, T.Y.: Granular computing on binary relations I: data mining and neighborhood systems. In: Proceedings of Rough sets in knowledge discovery (1998)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 2.5 International License (, which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

Authors and Affiliations

  • Zehua Zhang
    • 1
    Email author
  • Nan Zhang
    • 2
  • Caiming Zhong
    • 3
  • Litian Duan
    • 1
  1. 1.College of Computer Science and TechnologyTaiyuan University of TechnologyShanxiChina
  2. 2.School of Computer and Control EngineeringYantai UniversityShandongChina
  3. 3.College of Science and TechnologyNingbo UniversityZhejiangChina

Personalised recommendations