Skip to main content
SpringerLink
Log in

A hybrid artificial immune network for detecting communities in complex networks

  • Published:
Computing Aims and scope Submit manuscript

Abstract

One of the challenging problems when studying complex networks is the detection of sub-structures, called communities. Network communities emerge as dense parts, while they may have a few relationships to each other. Indeed, communities are latent among a mass of nodes and edges in a sparse network. This characteristic makes the community detection process more difficult. Among community detection approaches, modularity maximization has attracted much attention in recent years. In this paper, modularity density (D value) has been employed to discover real community structures. Due to the inadequacy of previous mathematical models in finding the correct number of communities, this paper first formulates a mixed integer non-linear program to detect communities without any need of prior knowledge about their number. Moreover, the mathematical models often suffer from NP-Hardness. In order to overcome this limitation, a new hybrid artificial immune network (HAIN) has been proposed in this paper. HAIN aims to use a network’s properties in an efficient way. To do so, this algorithm employs major components of the pure artificial immune network, hybridized with a well-known heuristic, to provide a powerful and parallel search mechanism. The combination of cloning and affinity maturation components, a strong local search routine, and the presence of network suppression and diversity are the main components. The experimental results on artificial and real-world complex networks illustrate that the proposed community detection algorithm provides a useful paradigm for robustly discovering community structures.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Agrawal G, Kempe D (2008) Modularity-maximizing graph communities via mathematical programming. Eur Phys J B 66(3):409–418. doi:10.1140/epjb/e2008-00425-1

    Article  MathSciNet  Google Scholar 

  2. Amiri B, Hossain L, Crawford JW (2011) An efficient multiobjective evolutionary algorithm for community detection in social networks. In: Evolutionary computation (CEC). IEEE Congress, New Orleans, pp 2193–2199. doi:10.1109/CEC.2011.5949886

  3. Amiri B, Hossain L, Crawford JW, Wigand RT (2013) Community detection in complex networks: multi-objective enhanced firefly algorithm. Knowl Syst 46:1–11. doi:10.1016/j.knosys.2013.01.004

    Article  Google Scholar 

  4. Arenas A, Díaz-Guilera A, Pérez-Vicente CJ (2006) Synchronization reveals topological scales in complex networks. Phys Rev Lett 96(11):114102. doi:10.1103/PhysRevLett.96.114102

    Article  Google Scholar 

  5. Bagrow JP, Bollt EM (2005) Local method for detecting communities. Phys Rev 72(4):046108. doi:10.1103/PhysRevE.72.046108

    Google Scholar 

  6. Bhagyesh VP, Nataraj PSV, Bhartiya S (2012) Global optimization of mixed-integer nonlinear (polynomial) programming problems: the Bernstein polynomial approach. Computing 94:325–343. doi:10.1007/s00607-011-0175-7

    Article  MATH  MathSciNet  Google Scholar 

  7. Bonanno G, Caldarelli G, Lillo F, Mantegna RN (2003) Topology of correlation-based minimal spanning trees in real and model markets. Phys Rev 68(4):046130. doi:10.1103/PhysRevE.68.046130

    Google Scholar 

  8. Castro LN, Timmis J (2002) Artificial immune systems: a new computational intelligence approach. Springer, Berlin

    Google Scholar 

  9. Chang MS, Hung LJ, Lin CR, Su PC (2013) Finding large k-clubs in undirected graphs. Computing 95:739–758. doi:10.1007/s00607-012-0263-3

    Article  MATH  MathSciNet  Google Scholar 

  10. Cheng Q, Liu Z, Huang J, Zhu C (2012) Hierarchical clustering based on hyper-edge similarity for community detection. In: Web intelligence and intelligent agent technology, IEEE, Macau. doi:10.1109/WI-IAT.2012.9

  11. Donath W, Hoffman A (1973) Lower bounds for the partitioning of graphs. IBM J Res Dev 17(5):420–425. doi:10.1147/rd.175.0420

  12. Everett MG, Borgatti SP (1994) Regular equivalence: general theory. J Math Soc 19(1):29–52

    Article  MATH  MathSciNet  Google Scholar 

  13. Fiedler M (1973) Algebraic connectivity of graphs. Czech Math J 23(2):298–305

    MathSciNet  Google Scholar 

  14. Flake GW, Lawrence S, Giles CL, Coetzee FM (2002) Self-organization and identification of web communities. IEEE Comput 35:66–71. doi:10.1109/2.989932

    Article  Google Scholar 

  15. Fortunato S, Barthélemy M (2007) Resolution limit in community detection. Proc Natl Acad Sci USA 104:36–41. doi:10.1073/pnas.0605965104

    Article  Google Scholar 

  16. Fortunato S (2010) Community detection in graphs. Phys Rep 486:75–174. doi:10.1016/j.physrep.2009.11.002

    Article  MathSciNet  Google Scholar 

  17. Freeman LC (1977) A set of measures of centrality based on betweenness. Sociometry 40:35–41

    Article  Google Scholar 

  18. Girvan M, Newman MEJ (2002) Community structure in social and biological networks. Proc Natl Acad Sci USA 99(12):7821–7826. doi:10.1073/pnas.122653799

    Article  MATH  MathSciNet  Google Scholar 

  19. Goldberg AV, Tarjan RE (1988) A new approach to the maximum flow problem. J ACM 35:921–940. doi:10.1145/48014.61051

    Article  MATH  MathSciNet  Google Scholar 

  20. Gong M, Fu B, Jiao L, Du H (2011) Memetic algorithm for community detection in networks. Phys Rev E84. doi:10.1103/PhysRevE.84.056101

  21. Gong M, Cai Q, Li Y, Ma J (2012) An improved memetic algorithm for community detection in complex networks. In: Evolutionary computations (CEC) IEEE congress on Brisbane. doi:10.1109/CEC.2012.6252971

  22. Gong M, Zhang LJ, Ma JJ, Jiao LC (2012) Community detection in dynamic social networks based on multiobjective immune algorithm. J Comput Sci Technol 27(3):455–467. doi:10.1007/s11390-012-1235-y

    Article  MATH  MathSciNet  Google Scholar 

  23. Guimerà R, Sales-Pardo M, Amaral LAN (2004) Modularity from fluctuations in random graphs and complex networks. Phys Rev E 70(2):025101. doi:10.1103/PhysRevE.70.025101

    Article  Google Scholar 

  24. Halalai R, Lemnaru C, Potolea R (2010) Distributed community detection in social networks with genetic algorithms. In: Intelligent communication and processing (ICCP), IEEE International Conference on Cluj-Napoca, pp 35–41. doi:10.1109/ICCP.2010.5606467

  25. Handcock MS, Raftery AE, Tantrum JM (2007) Model based clustering for social networks. J R Stat Soc A 170(2):301–354. doi:10.1111/j.1467-985X.2007.00471.x

  26. Hemmecke R, Köppe M, Lee J, Weismantel R (2010) Nonlinear integer programming. In: Jünger M et al (eds) 50 Years of integer programming 1958–2008. Springer, Berlin, pp 561–618

  27. Honghao C, Zuren F, Zhigang R (2013) Community detection using ant colony optimization. In: Evolutionary computation (CEC) IEEE Congress on Cancun. doi:10.1109/CEC.2013.6557944

  28. Hughes BD (1995) Random walks and random environments: random walks, vol 1. Clarendon Press, Oxford

    MATH  Google Scholar 

  29. Kernighan BW, Lin S (1970) An efficient heuristic procedure for partitioning graphs. Bell Syst Tech J 49:291–307. doi:10.1002/j.1538-7305.1970.tb01770.x

    Article  MATH  Google Scholar 

  30. Knuth DE (1993) The Stanford graph base: a platform for combinatorial computing. Addison-Wesley, Reading

    Google Scholar 

  31. Kumpula JM, Saramäki J, Kaski K, Kertész J (2007) Limited resolution and multiresolution methods in complex network community detection. In: Noise and stochastics in complex systems and finance in SPIE Conference Series, vol 6601

  32. Lancichinetti A, Fortunato S, Radicchi F (2008) Benchmark graphs for testing community detection algorithms. Phys l Rev E 78:046110. doi:10.1103/PhysRevE.78.046110

    Article  Google Scholar 

  33. Li X, Li D, Wang S, Tao Z (2007) Effective algorithm for detecting community structure in complex networks based on GA and clustering. Proc. Comput. Sci. ICCS, Beijing, China, pp 657–664. doi:10.1007/978-3-540-72586-2_95

  34. Li Z, Zhang S, Wang RS, Zhang XS, Chen L (2008) Quantitative function for community detection. Phys Rev E 77:036109. doi:10.1103/PhysRevE.77.036109

    Article  Google Scholar 

  35. Li J, Song Y (2013) A genetic algorithm for community detection in complex networks. Soft Comput 17(6):925–937. doi:10.1007/s11771-013-1611-y

    Article  Google Scholar 

  36. Liu X, Murata T (2010) Advanced modularity-specialized label propagation algorithm for detecting communities in networks. Phys A Stat Mech Appl 389(7):143–150. doi:10.1016/j.physa.2009.12.019

    Article  Google Scholar 

  37. Liu JX, Zeng J (2010) Community detection based on modularity density and genetic algorithm. In: 2010 International Conference on Computational Aspects of Social Networks (CASoN), pp 29–32. doi:10.1109/CASoN.2010.14

  38. Lorrain F, White H (1971) Structural equivalence of individuals in social networks. J Math Sociol 1:49–80. doi:10.1080/0022250X.1971.9989788

    Article  Google Scholar 

  39. Lusseau D, Schneider K, Boisseau OJ, Haase P, Slooten E, Dawson SM (2003) The bottlenose dolphin community of doubtful sound features a large proportion of long-lasting associations. Behav Ecol Sociobiol 54:396–405. doi:10.1007/s00265-003-0651-y

    Article  Google Scholar 

  40. Massen CP, Doye JPK (2005) Identifying communities within energy landscapes. Phys Rev E 71 doi:10.1103/PhysRevE.71.046101

  41. Medus A, Acuña G, Dorso CO (2005) Detection of community structures in networks via global optimization. Phys A Stat Mech Appl 358:593–604. doi:10.1016/j.physa.2005.04.022

    Article  Google Scholar 

  42. Mitrović M, Tadić B (2009) Spectral and dynamical properties in classes of sparse networks with mesoscopic in homogeneities. Phys Rev E 80(2):026123. doi:10.1103/PhysRevE.80.026123

    Article  Google Scholar 

  43. Nepusz T, Petróczi A, Négyessy L, Bazsó F (2008) Fuzzy communities and the concept of bridgeness in complex networks. Phys Rev E. doi:10.1103/PhysRevE.77.016107

  44. Newman MEJ, Girvan M (2004) Finding and evaluating community structure in networks. Phys Rev E. doi:10.1103/PhysRevE.69.026113

  45. Newman MEJ (2006) Finding community structure in networks using the eigenvectors of matrices. Phys Rev E. doi:10.1103/PhysRevE.74.036104

  46. Osman IH, Al-Ayoubi B (2005) MIC Analysis for Comparing Metaheuristics. In: Proceedings of the 6th Meta-heuristics International Conference, Vienna, Austria, August 22–26, pp 725–732

  47. Papadopoulos S, Skusa A, Vakali A, Kompatsiaris Y, Wagner N (2009) Bridge bounding: a local approach for efficient community discovery in complex networks. eprint arXiv:0902.0871

  48. Palla G, Derényi I, Farkas I, Vicsek T (2005) Uncovering the overlapping community structure of complex networks in nature and society. Nature 435:814–818. doi:10.1038/nature03607

    Article  Google Scholar 

  49. Raghavan UN, Albert R, Kumara S (2007) Near linear time algorithm to detect community structures in large-scale networks. Phys Rev E. doi:10.1103/PhysRevE.76.036106

  50. Reichardt J, Bornholdt S (2004) Detecting Fuzzy community structures in complex networks with a Potts model. Phys Rev Lett. doi:10.1103/PhysRevLett.93.218701

  51. Reichardt J, Bornholdt S (2006) When are networks truly modular? Phys D 224:20–26. doi:10.1016/j.physd.2006.09.009

    Article  MATH  MathSciNet  Google Scholar 

  52. Rosvall M, Bergstrom CT (2007) An information-theoretic framework for resolving community structure in complex networks. Proc Natl Acad Sci USA 104:7327–7331. doi:10.1073/pnas.0611034104

    Article  Google Scholar 

  53. Shang R, Bai J, Jiao L, Jin C (2010) Community detection based on modularity and an improved genetic algorithm. Phys A Stat Mech Appl 392(5):1215–1231. doi:10.1016/j.physa.2012.11.003

  54. Shi C, Yan Z, Cai Y, Wu B (2012) Multi-objective community detection in complex networks. Appl Soft Comput 12(2):850–859. doi:10.1016/j.asoc.2011.10.005

    Article  Google Scholar 

  55. Talbi E (2009) Metaheuristics from design to implementation. Wiley, Hoboken

    MATH  Google Scholar 

  56. Tasgin M, Bingol H (2006) Community detection in complex networks using genetic algorithm. In: ECCS ’06. Proceedings of the European Conference on Complex Systems

  57. Traag VA, Bruggeman J (2009) Community detection in networks with positive and negative links. Phys Rev. doi:10.1103/PhysRevE.80.036115

  58. White JG, Southgate E, Thompson JN, Brenner S (1986) The structure of the nervous system of the nematode C. elegans (aka ”The Mind of a Worm”). Phil Trans R Soc Lond 314:1–340. doi:10.1098/rstb.1986.0056

    Article  Google Scholar 

  59. Wu FY (1982) The Potts model. Rev Mod Phys 54(1):235–268. doi:10.1103/RevModPhys.54.235

  60. Xu G, Tsoka S, Papageorgiou LG (2007) Finding community structures in complex networks using mixed integer optimization. Eur Phys J B 60:231–239. doi:10.1140/epjb/e2007-00331-0

    Article  MATH  Google Scholar 

  61. Yang B, Liu J (2008) Discovering global network communities based on local centralities. ACM Trans Web 2(1):1–32

    Article  Google Scholar 

  62. Ye Z, Hu S, Yu J (2008) Adaptive clustering algorithm for community detection in complex networks. Phys Rev. doi:10.1103/PhysRevE.78.046115

  63. Yuruk N, Mete M, Xu X, Schweiger TAJ (2007) A divisive hierarchical structural clustering algorithm for networks. In: Data mining workshops, ICDM, Omaha, pp 441–448. doi:10.1109/ICDMW.2007.73

  64. Zachary WW (1977) An information flow model for conflict and fission in small groups. J Anthropol Res 33(4):452–473

    Google Scholar 

  65. Zanghi H, Ambroise C, Miele V (2008) Fast online graph clustering via Erdös-Rényi mixture. Pattern Recognit 41(12):3592–3599. doi:10.1016/j.patcog.2008.06.019

    Article  MATH  Google Scholar 

  66. Zhang XS, Wang RS (2008) Optimization analysis of modularity measures for network community detection. The Second International Symposium on Optimization and System Biology (OSB’08). Lijiang, China

    Google Scholar 

  67. Zhou H (2003) Network landscape from a Brownian particle’s perspective. Phys Rev. doi:10.1103/PhysRevE.67.041908

Download references

Author information

Authors and Affiliations

  1. Department of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran

    Amir-Mohsen Karimi-Majd & Mohammad Fathian

  2. The University of Sydney, New South Wales, Australia

    Babak Amiri

Authors
  1. Amir-Mohsen Karimi-Majd
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohammad Fathian
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Babak Amiri
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohammad Fathian.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Karimi-Majd, AM., Fathian, M. & Amiri, B. A hybrid artificial immune network for detecting communities in complex networks. Computing 97, 483–507 (2015). https://doi.org/10.1007/s00607-014-0433-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00607-014-0433-6

Keywords

Mathematics Subject Classification

Search

Navigation