Skip to main content

IbLT: An effective granular computing framework for hierarchical community detection


Mapping the vertices of network onto a tree helps to reveal the hierarchical community structures. The leading tree is a granular computing (GrC) model for efficient hierarchical clustering and it requires two elements: the distance between granules, and the density calculated in Euclidean space. For the non-Euclidean network data, the vertices need to be embedded in the Euclidean space before density calculation. This results in the marginalization of community centers. This paper proposes a new hierarchical community detection framework, called Importance-based Leading Tree (IbLT). Different from the density-based leading tree, IbLT calculates the structural similarity between vertices and the importance of the vertices respectively. It generates leading trees that match the structural features of the vertices, and thus, IbLT obtains more accurate results for the detection of hierarchical community structures. Experiments are conducted to evaluate the performance of the proposed novel IbLT-based method. On social network community detection task, the quantitative results show that this method achieves competitive accuracy.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Data Availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.


  1. Balakrishnan, S., Xu, M., Krishnamurthy, A., & et al. (2011). Noise thresholds for spectral clustering. In Proceedings of the 25th advances in neural information processing systems, curran associates, Inc. (pp. 954–962).

  2. Bindu, P., Mishra, R., & Thilagam, P.S. (2018). Discovering spammer communities in twitter. Journal of Intelligent Information Systems, 51(3), 503–527.

    Article  Google Scholar 

  3. Blin, L., Awan, A.J., & Heinis, T. (2018). Using neuromorphic hardware for the scalable execution of massively parallel, communication-intensive algorithms. In Proceedings of the 2018 IEEE/ACM international conference on utility and cloud computing companion (UCC Companion) (pp. 89–94). IEEE.

  4. Bryant, A., & Cios, K. (2017). Rnn-dbscan: a density-based clustering algorithm using reverse nearest neighbor density estimates. IEEE Transactions on Knowledge and Data Engineering, 30(6), 1109–1121.

    Article  Google Scholar 

  5. Chouchani, N., & Abed, M. (2020). Online social network analysis: detection of communities of interest. Journal of Intelligent Information Systems, 54 (1), 5–21.

    Article  Google Scholar 

  6. Clauset, A., Newman, M.E., & Moore, C. (2004). Finding community structure in very large networks. Physical Review E, 70(6), 066111.

    Article  Google Scholar 

  7. Danon, L., Diaz-Guilera, A., Duch, J., & et al. (2005). Comparing community structure identification. Journal of Statistical Mechanics: Theory and Experiment, 2005(09), P09008.

    Article  Google Scholar 

  8. Dasgupta, A., Hopcroft, J., Kannan, R., & et al. (2006). Spectral clustering by recursive partitioning. In Proceedings of the 14th European Symposium on Algorithms (pp. 256–267). Springer.

  9. Ding, Y., Yan, E., Frazho, A., & et al. (2009). Pagerank for ranking authors in co-citation networks. Journal of the American Society for Information Science and Technology, 60(11), 2229–2243.

    Article  Google Scholar 

  10. Ester, M., Kriegel, H.P., Sander, J., & et al. (1996). A density-based algorithm for discovering clusters in large spatial databases with noise. In Proceedings of the 2nd ACM SIGKDD international conference on knowledge discovery and data mining (pp. 226–231). ACM.

  11. Freeman, L.C. (1978). Centrality in social networks conceptual clarification. Social Networks, 1(3), 215–239.

    Article  Google Scholar 

  12. Gao, X., Bao, N., Liu, J., & et al. (2016). Scalable single-source simrank computation for large graphs. In Proceedings of the 2016 IEEE 22nd international conference on parallel and distributed systems (ICPADS), (pp. 1083–1091). IEEE.

  13. Girvan, M., & Newman, M.E. (2002). Community structure in social and biological networks. Proceedings of the National Academy of Sciences, 99(12), 7821–7826.

    MathSciNet  Article  Google Scholar 

  14. Gleich, D.F. (2015). Pagerank beyond the web. Siam Review, 57 (3), 321–363.

    MathSciNet  Article  Google Scholar 

  15. Guha, S., Rastogi, R., & Shim, K. (2000). Rock: a robust clustering algorithm for categorical attributes. Information Systems, 25(5), 345–366.

    Article  Google Scholar 

  16. Guha, S., Rastogi, R., & Shim, K. (2001). Cure: an efficient clustering algorithm for large databases. Information Systems, 26(1), 35–58.

    Article  Google Scholar 

  17. Hou, J., Gao, H., & Li, X. (2016). Dsets-dbscan: a parameter-free clustering algorithm. IEEE Transactions on Image Processing, 25(7), 3182–3193.

    MathSciNet  Article  Google Scholar 

  18. Jeh, G., & Widom, J. (2002). Simrank: a measure of structural-context similarity. In Proceedings of the 8th ACM SIGKDD international conference on knowledge discovery and data mining (pp. 538–543). ACM.

  19. Karypis, G., Han, E.H., & Kumar, V. (1999). Chameleon: Hierarchical clustering using dynamic modeling. Computer, 32(8), 68–75.

    Article  Google Scholar 

  20. Kleinberg, J. (2001). Small-world phenomena and the dynamics of information. In Proceedings of the 14th international conference on neural information processing systems: natural and synthetic (pp. 431–438). MIT Press.

  21. Kobren, A., Monath, N., Krishnamurthy, A., & et al. (2017). A hierarchical algorithm for extreme clustering. In Proceedings of the 23rd ACM SIGKDD international conference on knowledge discovery and data mining (pp. 255–264). ACM.

  22. Kumar, S., Panda, B., & Aggarwal, D. (2020). Community detection in complex networks using network embedding and gravitational search algorithm. Journal of Intelligent Information Systems, 57(1), 51–72.

    Article  Google Scholar 

  23. Kusumoto, M., Maehara, T., & Ki, K. (2014). Scalable similarity search for simrank. In Proceedings of the 2014 ACM SIGMOD international conference on management of data (pp. 325–336). ACM.

  24. Lancichinetti, A., Fortunato, S., & Radicchi, F. (2008). Benchmark graphs for testing community detection algorithms. Physical Review E, 78(4), 046110.

    Article  Google Scholar 

  25. Li, D., Liu, C., & Gan, W. (2009). A new cognitive model: Cloud model. International Journal of Intelligent Systems, 24(3), 357–375.

    Article  Google Scholar 

  26. Lv, Y., Ma, T., Tang, M., & et al. (2016). An efficient and scalable density-based clustering algorithm for datasets with complex structures. Neurocomputing, 171, 9–22.

    Article  Google Scholar 

  27. Lyzinski, V., Tang, M., Athreya, A., & et al. (2016). Community detection and classification in hierarchical stochastic blockmodels. IEEE Transactions on Network Science and Engineering, 4(1), 13–26.

    MathSciNet  Article  Google Scholar 

  28. Mislove, A., Marcon, M., Gummadi, K.P., & et al. (2007). Measurement and analysis of online social networks. In Proceedings of the 7th ACM SIGCOMM conference on internet measurement (pp. 29–42). ACM.

  29. Moody, J., & White, D.R. (2003). Structural cohesion and embeddedness: a hierarchical concept of social groups. American Sociological Review, 68 (1), 103–127.

    Article  Google Scholar 

  30. Murtagh, F., & Contreras, P. (2012). Algorithms for hierarchical clustering: an overview. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, 2(1), 86–97.

    Google Scholar 

  31. Page, L., Brin, S., Motwani, R., & et al. (1999). The pagerank citation ranking: Bringing order to the web. Tech. rep., Stanford InfoLab.

  32. Pawlak, Z. (1998). Granularity of knowledge, indiscernibility and rough sets. In Proceedings of the 1998 IEEE international conference on fuzzy systems proceedings (pp. 106–110). IEEE.

  33. Pedrycz, W. (2011). The principle of justifiable granularity and an optimization of information granularity allocation as fundamentals of granular computing. Journal of Information Processing Systems, 7(3), 397–412.

    Article  Google Scholar 

  34. Perozzi, B., Al-Rfou, R., & Skiena, S. (2014). Deepwalk: Online learning of social representations. In Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (pp. 701–710). ACM.

  35. Pons, P., & Latapy, M. (2005). Computing communities in large networks using random walks. In Proceedings of the 20th international symposium on computer and information sciences (pp. 284–293). Springer.

  36. Qian, Y., Liang, J., Yao, Y., & et al. (2010). Mgrs: a multi-granulation rough set. Information Sciences, 180(6), 949–970.

    MathSciNet  Article  Google Scholar 

  37. Qinghua Zhang, X.L., & Wang, G. (2008). Hierarchical structure analysis of fuzzy quotient space. Pattern Recognition and Artificial Intelligence [CN], 21 (5), 627–634.

    Google Scholar 

  38. Raghavan, U.N., Albert, R., & Kumara, S. (2007). Near linear time algorithm to detect community structures in large-scale networks. Physical Review E, 76(3), 036106.

    Article  Google Scholar 

  39. Ram, A., Sharma, A., Jalal, A.S., & et al. (2009). An enhanced density based spatial clustering of applications with noise. In Proceedings of 2009 IEEE international advance computing conference (pp. 1475–1478). IEEE.

  40. Sadi, F., Sweeney, J., McMillan, S., & et al. (2018). Pagerank acceleration for large graphs with scalable hardware and two-step spmv. In Proceedings of the 2018 IEEE high performance extreme computing conference (HPEC) (pp. 1–7). IEEE.

  41. Sarma, A.D., Molla, A.R., Pandurangan, G., & et al. (2013). Fast distributed pagerank computation. In Proceedings of the 14th international conference on distributed computing and networking (pp. 11–26). Springer.

  42. Vadapalli, S., Valluri, S.R., & Karlapalem, K. (2006). A simple yet effective data clustering algorithm. In Proceedings of the 6th international conference on data mining (pp. 1108–1112). IEEE.

  43. Wang, G. (2017). Dgcc: data-driven granular cognitive computing. Granular Computing, 2(4), 343–355.

    Article  Google Scholar 

  44. Wang, G., Yang, J., & Xu, J. (2017). Granular computing: from granularity optimization to multi-granularity joint problem solving. Granular Computing, 2(3), 105–120.

    Article  Google Scholar 

  45. Wang, R., Zhang, W., Deng, H., & et al. (2013). Discover community leader in social network with pagerank. In Proceedings of the 4th international conference in swarm intelligence (pp. 154–162). Springer.

  46. Xu, J., Wang, G., & Deng, W. (2016). Denpehc: Density peak based efficient hierarchical clustering. Information Sciences, 373, 200–218.

    Article  Google Scholar 

  47. Xu, J., Wang, G., Li, T., & et al. (2017a). Fat node leading tree for data stream clustering with density peaks. Knowledge-Based Systems, 120, 99–117.

    Article  Google Scholar 

  48. Xu, J., Wang, G., Li, T., & et al. (2017b). Local-density-based optimal granulation and manifold information granule description. IEEE Transactions on Cybernetics, 48(10), 2795–2808.

    Article  Google Scholar 

  49. Xu, J., Li, T., Wu, Y., & et al. (2021). Lapoleaf: Label propagation in an optimal leading forest. Information Sciences, 575, 133–154.

    MathSciNet  Article  Google Scholar 

  50. Yang, J., & Leskovec, J. (2015). Defining and evaluating network communities based on ground-truth. Knowledge and Information Systems, 42(1), 181–213.

    Article  Google Scholar 

  51. Yang, Z., Algesheimer, R., & Tessone, C.J. (2016). A comparative analysis of community detection algorithms on artificial networks. Scientific Reports, 6(1), 1–18.

    Article  Google Scholar 

  52. Yao, J.T., Vasilakos, A.V., & Pedrycz, W. (2013). Granular computing: perspectives and challenges. IEEE Transactions on Cybernetics, 43(6), 1977–1989.

    Article  Google Scholar 

  53. Yao, Y., & Zhao, L. (2012). A measurement theory view on the granularity of partitions. Information Sciences, 213, 1–13.

    MathSciNet  Article  Google Scholar 

  54. Yao, Y., et al. (2000). Granular computing: basic issues and possible solutions. In Proceedings of the 5th joint conference on information sciences, association for intelligent machinery, pp 186–189.

  55. Young, S.J., & Scheinerman, E.R. (2007). Random dot product graph models for social networks. In Proceedings of the 5th international workshop on algorithms and models for the web-graph (pp. 138–149). Springer.

  56. Yu, W., Lin, X., & Le, J. (2010). Taming computational complexity: Efficient and parallel simrank optimizations on undirected graphs. In Proceedings of the 2010 international conference on web-age information management (pp. 280–296). Springer.

  57. Yu, W., Lin, X., Zhang, W., & et al. (2019). Simrank*: effective and scalable pairwise similarity search based on graph topology. The VLDB Journal, 28(3), 401–426.

    Article  Google Scholar 

  58. Zachary, W.W. (1977). An information flow model for conflict and fission in small groups. Journal of Anthropological Research, 33(4), 452–473.

    Article  Google Scholar 

  59. Zadeh, L.A. (1997). Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets and Systems, 90 (2), 111–127.

    MathSciNet  Article  Google Scholar 

  60. Zhang, L., & Zhang, B. (2004). The quotient space theory of problem solving. Fundamenta Informaticae, 59(2-3), 287–298.

    MathSciNet  MATH  Google Scholar 

  61. Zhang, T., Ramakrishnan, R., & Livny, M. (1997). Birch: a new data clustering algorithm and its applications. Data Mining and Knowledge Discovery, 1 (2), 141–182.

    Article  Google Scholar 

Download references


The authors would like to thank the editors and anonymous reviewers for their constructive comments. This work is supported in part by the National Science Foundation of China (grant no. 61936001, 61772096, 61966005), Graduate Research and Innovation Project Plan of Chongqing Municipal Education Commission (grant no. CYB18174), and the Doctor Training Program of Chongqing University of Posts and Telecommunications (grant no. BYJS201809).

Author information



Corresponding author

Correspondence to Guoyin Wang.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Fu, S., Wang, G., Xu, J. et al. IbLT: An effective granular computing framework for hierarchical community detection. J Intell Inf Syst (2021).

Download citation


  • Rough set
  • Granular computing
  • Network representation learning
  • Social networks