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Journal of Combinatorial Optimization

, Volume 30, Issue 3, pp 747–767 | Cite as

A near-optimal adaptive algorithm for maximizing modularity in dynamic scale-free networks

  • Thang N. Dinh
  • Nam P. Nguyen
  • Md Abdul Alim
  • My T. Thai
Article

Abstract

We introduce A\(^3\)CS, an adaptive framework with approximation guarantees for quickly identifying community structure in dynamic networks via maximizing Modularity Q. Our framework explores the advantages of the power-law distribution property found in many real-world complex systems. The framework is scalable for very large networks, and more excitingly, possesses approximation factors to ensure the quality of its detected community structure. To the best of our knowledge, this is the first framework that achieves approximation guarantees for the NP-hard Modularity maximization problem, especially on dynamic scale-free networks. To certify our approach, we conduct extensive experiments in comparison with other adaptive methods on both synthesized networks with known community structures and real-world traces including ArXiv e-print citation and Facebook social networks. Excellent empirical results not only confirm our theoretical results but also promise the practical applicability of A\(^3\)CS in a wide range of dynamic networks.

Keywords

Adaptive approximation algorithm Community structure  Modularity Social networks 

Notes

Acknowledgments

This work is partially supported by NSF CAREER AWARD 0953284 and HDTRA-1-10-1-0050.

References

  1. Agarwal G, Kempe D (2008) Modularity-maximizing graph communities via mathematical programming. Eur Phys J B 66:409–418Google Scholar
  2. Aiello W, Chung F, Lu L (2000) A random graph model for massive graphs. In: STOC ’00. ACM, New York, NY, USAGoogle Scholar
  3. Aiello W, Chung F, Lu L (2001) Random evolution in massive graphs. In: Handbook of massive data sets. Kluwer Academic Publishers, NorwellGoogle Scholar
  4. Albert R, Jeong H, Barabasi A (2000) Error and attack tolerance of complex networks. Nature 406:378–482Google Scholar
  5. Bansal N, Blum A, Chawla S (2002) Correlation clustering. In: Annual IEEE symposium on foundations of computer science (FOCS), vol 0, p 238. doi: 10.1109/SFCS.2002.1181947
  6. Barabasi A, Albert R, Jeong H (2000) Scale-free characteristics of random networks: the topology of the world-wide web. Phys A 281:69–77Google Scholar
  7. Barabasi AL, Jeong H, Nda Z, Ravasz E, Schubert A, Vicsek T (2002) Evolution of the social network of scientific collaborations. Phys A 311:590–614Google Scholar
  8. Bianconi G, Barabasi AL (2001) Competition and multiscaling in evolving networks. EPL (Europhysics Letters) 54(4):436. http://stacks.iop.org/0295-5075/54/i=4/a=436
  9. Blondel VD, Guillaume JL, Lambiotte R, Lefebvre E (2008) Fast unfolding of communities in large networks. J Stat Mech Theory Exp 2008(10):P10008Google Scholar
  10. 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):172–188Google Scholar
  11. Clauset A, Newman MEJ, Moore C (2004) Finding community structure in very large networks. Phys Rev E 70(6):066111Google Scholar
  12. DasGupta, B, Desai D (2012) On the complexity of newman’s community finding approach for biological and social networks. J Comput Syst Sci 79(1):50–67. doi: 10.1016/j.jcss.2012.04.003
  13. Dinh TN, Thai MT (2011) Finding community structure with performance guarantees in scale-free networks. In: SocialCom/PASSAT, pp 888–891Google Scholar
  14. Dinh TN, Xuan Y, Thai MT (2009) Towards social-aware routing in dynamic communication networks. IPCCCGoogle Scholar
  15. Faloutsos M, Faloutsos P, Faloutsos C (1999) On power-law relationships of the internet topology. In: Proceedings of the conference on applications, technologies, architectures, and protocols for computer communication, SIGCOMM ’99, pp 251–262. ACM, New York, NY, USA. doi: 10.1145/316188.316229
  16. Ferrante A (2006) Hardness and approximation algorithms of some graph problemsGoogle Scholar
  17. Fortunato S, Barthelemy M (2007) Resolution limit in community detection. Proc Natl Acad Sci USA 104(1):36–41Google Scholar
  18. Giotis I, Guruswami V (2006) Correlation clustering with a fixed number of clusters. Theory Comput 2(1):249–266. doi: 10.4086/toc.2006.v002a013 Google Scholar
  19. Good BH, de Montjoye YA, Clauset A (2010) Performance of modularity maximization in practical contexts. Phys Rev E 81, 046,106. doi: 10.1103/PhysRevE.81.046106
  20. Hui P, Crowcroft J, Yoneki E (2011) Bubble rap: social-based forwarding in delay-tolerant networks. IEEE Trans Mobile Comput 10(11):1576–1589. doi: 10.1109/TMC.2010.246 Google Scholar
  21. Lancichinetti A, Fortunato S (2009) Community detection algorithms: a comparative analysis. Phys Rev E 80(5), 056117. doi: 10.1103/PhysRevE.80.056117
  22. Lancichinetti A, Radicchi F, Ramasco JJ, Fortunato S (2011) Finding statistically significant communities in networks. PLoS ONE 6, e17249Google Scholar
  23. Lin Y, Chi Y, Zhu S, Sundaram H, Tseng BL, Facetnet: a framework for analyzing communities and their evolutions in dynamic networks. WWW (2008)Google Scholar
  24. Newman MEJ (2003) The structure and function of complex networks. SIAM Rev 45(2):167–256zbMATHMathSciNetCrossRefGoogle Scholar
  25. Newman MEJ (2006) Modularity and community structure in networks. Proc Natl Acad Sci USA 103(23):8577–8582Google Scholar
  26. Nguyen N, Dinh T, Xuan Y, Thai M (2011) Adaptive algorithms for detecting community structure in dynamic social networks. In: INFOCOM, 2011 Proceedings IEEE, pp 2282–2290. doi: 10.1109/INFCOM.2011.5935045
  27. Noack A (2009) Modularity clustering is force-directed layout. Phys Rev E 79, 026,102. doi: 10.1103/PhysRevE.79.026102
  28. Pásztor B, Mottola L, Mascolo C, Picco G, Ellwood S, Macdonald D (2010) Selective reprogramming of mobile sensor networks through social community detection. In: Proceedings of EWSN, vol 5970, pp 178–193. Springer, BerlinGoogle Scholar
  29. Tantipathananandh C, Berger-Wolf T (2009) Constant-factor approximation algorithms for identifying dynamic communities. In: Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining, KDD ’09. ACM, New York, NY, USA, pp 827–836. doi: 10.1145/1557019.1557110.
  30. Viswanath B, Mislove A, Cha M, Gummadi KP (2009) On the evolution of user interaction in facebook. In: 2nd ACM SIGCOMM Workshop on Social NetworksGoogle Scholar
  31. Yu H, Kaminsky M, Gibbons PB, Flaxman A (2006) Sybilguard: defending against sybil attacks via social networks. In: Proceedings of the ACM SIGCOMM 2006 conference, SIGCOMM ’06, pp 267–278. ACM, New York, NY, USA. doi: 10.1145/1159913.1159945.
  32. Zhu Z, Cao G, Zhu S, Ranjan S, Nucci A (2009) A social network based patching scheme for worm containment in cellular networks. In: INFOCOM 2009, IEEE, pp 1476–1484. doi: 10.1109/INFCOM.2009.5062064.

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Thang N. Dinh
    • 1
  • Nam P. Nguyen
    • 1
    • 2
  • Md Abdul Alim
    • 1
  • My T. Thai
    • 1
  1. 1.Deparment of Computer and Information Science and EngineeringUniversity of FloridaGainesvilleUSA
  2. 2.Computer and Information Sciences DepartmentTowson UniversityTowsonUSA

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