Applied Intelligence

, Volume 49, Issue 2, pp 689–702 | Cite as

A fast divisive community detection algorithm based on edge degree betweenness centrality

  • Majid Arasteh
  • Somayeh AlizadehEmail author


Many complex systems in the real world such as social networks can be modeled by complex networks. The complex network analysis and especially community detection is an important research topic in graph analysis that aims to identify the structure of a graph and its similar groups of nodes. In recent years, various algorithms such as Girvan and Newman’s method (GN) is introduced which is based on a divisive approach for graph clustering. Although GN is a highly popular and widely used method, it suffers from scalability and computational complexity. GN needs O(m3) and O(m3 + m3logm) time to detects communities in unweighted and weighted graphs respectively. Hence, in this paper, a faster method is suggested that detects communities in O(m2) for both weighted and unweighted graphs. In this paper, firstly, we define degree for each edge and then we propose a new and fast approach for the calculation of edges betweenness that is based on edge degree centrality. Furthermore, in order to boost the speed of the algorithm, we suggest instead of just one edge, multiple edges can be removed in each iteration. Since the proposed method wants to enhance the GN method, in the evaluation section the quality of detected communities, the accuracy and speed of the suggested method are assessed by the comparison with the GN method. Results prove that our proposed method is extremely faster than plain GN and the detected communities often have better quality than the plain GN method. Furthermore, we compare our proposed method with meta-heuristic algorithms which are a novel approach for community detection. Results clarify that the suggested method is notably faster, scalable, stable, reliable, and efficient than meta-heuristic algorithms.


Community detection Complex network Edge centrality Betweenness 


  1. 1.
    Chapela V, et al (2015) Mathematical foundations: complex networks and graphs (a review). Intentional risk management through complex networks analysis. Springer, Cham, pp 9–36Google Scholar
  2. 2.
    Mochón M (2016) Social network analysis and big data tools applied to the systemic risk supervision. Int J Interact Multimed Artif Intell (Ijimai) 3(6):34–37Google Scholar
  3. 3.
    Lee H, Shao B, Kang U (2015) Fast graph mining with HBase. Inform Sci 315:56–66MathSciNetGoogle Scholar
  4. 4.
    Radicchi F, Castellano C, Cecconi F, Loreto V, Parisi D (2004) Defining and identifying communities in networks. Proc Natl Acad Sci 101(9):2658–2663Google Scholar
  5. 5.
    Fortunato S (2010) Community detection in graphs. Phys Rep 486(3–5):75–174MathSciNetGoogle Scholar
  6. 6.
    Khan K, Sahai A, Campus A (2012) A fuzzy c-means bi-sonar-based metaheuristic optimization algorithm. Int J Artif Intell Interac Multimed (IJIMAI) 1(7):26–32Google Scholar
  7. 7.
    Papadopoulos S, Kompatsiaris Y, Vakali A, Spyridonos P (2012) Community detection in social media. Data Min Knowl Disc 24(3):515–554Google Scholar
  8. 8.
    Plantié M, Crampes M (2013) Survey on social community detection. In social media retrieval. Springer, London, pp 65–85Google Scholar
  9. 9.
    Brandes U, Delling D, Gaertler M, Gorke R, Hoefer M, Nikoloski Z, Wagner D (2008) On modularity clustering. IEEE Trans Knowl Data Eng 20(2):172–188zbMATHGoogle Scholar
  10. 10.
    Waltman L, Van Eck N (2013) A smart local moving algorithm for large-scale modularity-based community detection. Europ Phys J B 86(11):471Google Scholar
  11. 11.
    Schaeffer S (2007) Graph clustering. Comput Sci Rev 1(1):27–64zbMATHGoogle Scholar
  12. 12.
    Bedi P, Sharma C (2016) Community detection in social networks. Wiley Interdiscip Rev Data Mining Knowl Discov 6(3):115–135Google Scholar
  13. 13.
    Newman M (2004) Fast algorithm for detecting community structure in networks. Phys Rev E 69(6):066133Google Scholar
  14. 14.
    Clauset A, Newman M, Moore C (2004) Finding community structure in very large networks. Phys Rev E 70(6):066111Google Scholar
  15. 15.
    Newman M (2004) Analysis of weighted networks. Phys Rev E 70(5):056131Google Scholar
  16. 16.
    Hurajová J, Madaras T (2016) Revising the Newman-Girvan algorithm. In: ITAT Proceedings, CEUR workshop proceedings, pp 200–205Google Scholar
  17. 17.
    Kernighan B, Lin S (1970) An efficient heuristic procedure for partitioning graphs. Bell Syst Tech J 49 (2):291–307zbMATHGoogle Scholar
  18. 18.
    Blondel V, Guillaume J, Lambiotte R, Lefebvre E (2008) Fast unfolding of communities in large networks. J Statist Mech Theory Exper 10:10008Google Scholar
  19. 19.
    JSuaris P, Kedem G (1988) An algorithm for quadrisection and its application to standard cell placement. IEEE Trans Circ Syst 35(3):294–303Google Scholar
  20. 20.
    Rotta R, Noack A (2011) Multilevel local search algorithms for modularity clustering. J Exper Algor (JEA) 16:2–3MathSciNetzbMATHGoogle Scholar
  21. 21.
    Lu H, Halappanavar M, Kalyanaraman A (2015) Parallel heuristics for scalable community detection. Parallel Comput 47:19–37MathSciNetGoogle Scholar
  22. 22.
    Liu W, Yue K, Wu H, Fu X, Zhang Z, Huang W (2018) Markov-network based latent link analysis for community detection in social behavioral interactions. Appl Intell 48(8):2081–2096Google Scholar
  23. 23.
    Guimera R, Sales-Pardo M, Amaral LA (2004) Modularity from fluctuations in random graphs and complex networks. Phys Rev E 70(2):025101Google Scholar
  24. 24.
    Massen C, Doye J (2005) Identifying communities within energy landscapes. Phys Rev E 71(4):046101Google Scholar
  25. 25.
    Duch J, Arenas A (2005) Community detection in complex networks using extremal optimization. Phys Rev E 72(2):027104Google Scholar
  26. 26.
    Tasgin M, Herdagdelen A, Bingol H (2007) Community detection in complex networks using genetic algorithms. arXiv:0711.0491
  27. 27.
    Pizzuti C (2008) Ga-net: a genetic algorithm for community detection in social networks. In: International conference on parallel problem solving from nature. Springer, Berlin, pp 1081–1090Google Scholar
  28. 28.
    Shang R, Bai J, Jiao L, Jin C (2013) Community detection based on modularity and an improved genetic algorithm. Physica A: Statist Mech Appl 392(5):1215–1231Google Scholar
  29. 29.
    Gong M, Fu B, Jiao L, Du H (2011) Memetic algorithm for community detection in networks. Phys Rev E 84(5):056101Google Scholar
  30. 30.
    Fan H, Zhong Y, Zeng G (2018) Overlapping community detection based on discrete biogeography optimization. Appl Intell 48(5):1314–1326Google Scholar
  31. 31.
    Guendouz M, Amine A, Hamou R (2017) A discrete modified fireworks algorithm for community detection in complex networks. Appl Intell 46(2):373–385Google Scholar
  32. 32.
    Pizzuti C (2012) A multiobjective genetic algorithm to find communities in complex networks. IEEE Trans Evol Comput 16(3):418–430Google Scholar
  33. 33.
    Shi C, Yan Z, Cai Y, Wu B (2012) Multi-objective community detection in complex networks. Appl Soft Comput 12(2):850–859Google Scholar
  34. 34.
    Gong M, Ma L, Zhang Q, Jiao L (2012) Community detection in networks by using multiobjective evolutionary algorithm with decomposition. Physica A: Statist Mech Appl 391(15):4050–4060Google Scholar
  35. 35.
    Gong M, Cai Q, Chen X, Ma L (2014) Complex network clustering by multiobjective discrete particle swarm optimization based on decomposition. IEEE Trans Evol Comput 18(1):82–97Google Scholar
  36. 36.
    Meza J, Espitia H, Montenegro C, Giménez E, González-Crespo R (2017) MOVPSO: vortex multi-objective particle swarm optimization. Appl Soft Comput 52:1042–1057Google Scholar
  37. 37.
    Zhou X, Zhao X, Liu Y (2018) A multiobjective discrete bat algorithm for community detection in dynamic networks. Appl Intell 48(9):3081–3093Google Scholar
  38. 38.
    Li Z, He L, Li Y (2016) A novel multiobjective particle swarm optimization algorithm for signed network community detection. Appl Intell 44(3):621–633Google Scholar
  39. 39.
    Brandes U, Fleischer D (2005) Centrality measures based on current flow. In: Annual symposium on theoretical aspects of computer science. Springer, Berlin, pp 533–544Google Scholar
  40. 40.
    Mason O, Verwoerd M (2007) Graph theory and networks in biology. IET Syst Biol 1(2):89–119Google Scholar
  41. 41.
    Estrada E (2006) Virtual identification of essential proteins within the protein interaction network of yeast. Proteomics 6(1):35–40Google Scholar
  42. 42.
    Freeman L (1977) A set of measures of centrality based on betweenness. Sociometry 40(1):35–41Google Scholar
  43. 43.
    Newman ME (2005) A measure of betweenness centrality based on random walks. Soc Netw 27(1):39–54Google Scholar
  44. 44.
    Ahajjam S, El Haddad M, Badir H (2018) A new scalable leader-community detection approach for community detection in social networks. Soc Netw 54:41–49Google Scholar
  45. 45.
    Lancichinetti A, Fortunato S (2009) Community detection algorithms: a comparative analysis. Phys Rev E 80(5):056117Google Scholar
  46. 46.
    Newman M, Girvan M (2004) Finding and evaluating community structure in networks. Phys Rev E 69 (2):026113Google Scholar
  47. 47.
    Brandes U (2001) A faster algorithm for betweenness centrality. J Math Sociol 25(2):163–177zbMATHGoogle Scholar
  48. 48.
    Brandes U (2008) On variants of shortest-path betweenness centrality and their generic computation. Soc Netw 30(2):136–145Google Scholar
  49. 49.
    Wagner S, Wagner D (2007) Comparing clusterings: an overview Karlsruhe. Universität Karlsruhe, Fakultät für InformatikGoogle Scholar
  50. 50.
    Chakraborty T, Dalmia A, Mukherjee A, Ganguly N (2017) Metrics for community analysis: a survey. ACM Comput Surv (CSUR) 50(4):54Google Scholar
  51. 51.
    Talbi EG (2009) Metaheuristics: from design to implementation. mplementation, vol 74. WileyGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of Industrial EngineeringK. N. Toosi University of TechnologyTehranIran

Personalised recommendations