Peer-to-Peer Networking and Applications

, Volume 10, Issue 2, pp 411–420 | Cite as

Finding overlapping communities based on Markov chain and link clustering

  • Xiaoheng Deng
  • Genghao Li
  • Mianxiong Dong
  • Kaoru Ota


Since community structure is an important feature of complex network, the study of community detection has attracted more and more attention in recent years. Despite most researchers focus on identifying disjoint communities, communities in many real networks often overlap. In this paper, we proposed a novel MCLC algorithm to discover overlapping communities, which using random walk on the line graph and attraction intensity. Unlike traditional random walk starting from a node, our random walk starts from a link. First we transform an undirected network graph to a weighted line graph, and then random walks on this line graph can be associated with a Markov chain. By calculating the transition probability of the Markov chain, we obtain the similarity between link pairs. Next the links can be clustered into “link communities” by a linkage method, and these nodes between link communities can be overlapping nodes. When converting the “link communities” into the “node communities”, we make a definition of attraction intensity to control the overlapping size. Finally the detected communities are permitted overlapped. Experiments on synthetic networks and some real world networks validate the effectiveness and efficiency of the proposed algorithm. Comparing overlapping modularity Q o v with other related algorithms, the results of this algorithm are satisfactory.


Community detection Random walk Link community Overlapping community 



The author gratefully acknowledges support from National Natural Science Foundation of China projects of grant No. 61272149, 61379058, 61379057, 61350011, JSPS A3 Foresight Program, and JSPS KAKENHI Grant Number 26730056, 15K15976.


  1. 1.
    Strogatz SH (2001) Exploring complex networks. Nature 410(6825):268–276CrossRefGoogle Scholar
  2. 2.
    Albert R, Barabási AL (2002) Statistical mechanics of complex networks. Rev Mod Phys 74(1):47MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Newman ME, Girvan M (2004) Finding and evaluating community structure in networks. Physical review E 69(2):026113CrossRefGoogle Scholar
  4. 4.
    Radicchi F, Castellano C, Cecconi F, Loreto V, Parisi D (2004) Defining and identifying communities in networks. Proc Natl Acad Sci USA 101(9):2658–2663CrossRefGoogle Scholar
  5. 5.
    Rosvall M, Bergstrom CT (2008) Maps of random walks on complex networks reveal community structure. Proc Natl Acad Sci 105(4):1118–1123CrossRefGoogle Scholar
  6. 6.
    Mianxiong D, Kimata T, Sugiura K, Zettsu K (2014) Quality-of-experience (qoe) in emerging mobile social networks. IEICE TRANSACTIONS on Information and Systems 97(10):2606–2612Google Scholar
  7. 7.
    Ping Y, Cao Z, Zhu H (2014) Sybil-aware least cost rumor blocking in social networks. In: Global communications conference (GLOBECOM), 2014 IEEE, IEEE, pp 692–697Google Scholar
  8. 8.
    Li M., Zhu H., Gao Z., Chen S., Yu L., Hu S., Ren K. (2014) All your location are belong to us: Breaking mobile social networks for automated user location tracking. In: Proceedings of the 15th ACM international symposium on mobile ad hoc networking and computing, ACM, pp 43–52Google Scholar
  9. 9.
    Zhu H, Lin X, Lu R, Fan Y, Shen X (2009) Smart A secure multilayer credit-based incentive scheme for delay-tolerant networks. IEEE Trans Veh Technol 58(8):4628–4639CrossRefGoogle Scholar
  10. 10.
    Du S, Zhu H, Li X, Ota K, Dong M (2013) Mixzone in motion: achieving dynamically cooperative location privacy protection in delay-tolerant networks. IEEE Trans Veh Technol 62(9):4565–4575CrossRefGoogle Scholar
  11. 11.
    Zhu H, Du S, Gao Z, Dong M, Cao Z (2014) A probabilistic misbehavior detection scheme toward efficient trust establishment in delay-tolerant networks. IEEE Trans Parallel Distrib Syst 25(1):22–32CrossRefGoogle Scholar
  12. 12.
    Tao J, Tan C, Zhang Z, He J, Xu Y (2015) Opportunistic forwarding based on the weighted social characteristics in msns. In: Communications (ICC), 2015 IEEE international conference on IEEE, pp 6318–6323Google Scholar
  13. 13.
    Wang T, Chen Z, Li K, Deng X, Li D (2014) Memory does not necessarily promote cooperation in dilemma games. Physica A: Statistical Mechanics and its Applications 395:218–227MathSciNetCrossRefGoogle Scholar
  14. 14.
    Jonsson PF, Cavanna T, Zicha D, Bates PA (2006) Cluster analysis of networks generated through homology: automatic identification of important protein communities involved in cancer metastasis. BMC bioinformatics 7(1):2CrossRefGoogle Scholar
  15. 15.
    Krause AE, Frank KA, Mason DM, Ulanowicz RE, Taylor WW (2003) Compartments revealed in food-web structure. Nature 426(6964):282–285CrossRefGoogle Scholar
  16. 16.
    Piccardi C, Calatroni L, Bertoni F (2010) Communities in italian corporate networks. Physica A: Statistical Mechanics and its Applications 389(22):5247–5258CrossRefGoogle Scholar
  17. 17.
    Fortunato S (2010) Community detection in graphs. Phys Rep 486(3):75–174MathSciNetCrossRefGoogle Scholar
  18. 18.
    Kernighan BW, Lin S (1970) An efficient heuristic procedure for partitioning graphs. Bell system technical journal 49(2):291–307CrossRefzbMATHGoogle Scholar
  19. 19.
    Pothen A, Simon HD, Liou KP (1990) Partitioning sparse matrices with eigenvectors of graphs. SIAM J Matrix Anal Appl 11(3):430–452MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Hastie T, Tibshirani R, Friedman J, Franklin J (2005) The elements of statistical learning: data mining, inference and prediction. Math Intell 27(2):83–85Google Scholar
  21. 21.
    Blondel VD, Guillaume JL, Lambiotte R, Lefebvre E (2008) Fast unfolding of communities in large networks. J Stat Mech Theory Exp 2008(10):10008CrossRefGoogle Scholar
  22. 22.
    Palla G, Derényi I, Farkas I, Vicsek T (2005) Uncovering the overlapping community structure of complex networks in nature and society. Nature 435(7043):814–818CrossRefGoogle Scholar
  23. 23.
    Lancichinetti A, Fortunato S, Kertész J (2009) Detecting the overlapping and hierarchical community structure in complex networks. New J Phys 11(3):033015CrossRefGoogle Scholar
  24. 24.
    Wang X, Jiao L, Wu J (2009) Adjusting from disjoint to overlapping community detection of complex networks. Physica A: Statistical Mechanics and its Applications 388(24):5045–5056CrossRefGoogle Scholar
  25. 25.
    Ahn YY, Bagrow JP, Lehmann S (2010) Link communities reveal multiscale complexity in networks. Nature 466(7307):761–764CrossRefGoogle Scholar
  26. 26.
    Havemann F, Heinz M, Struck A, Gläser J (2011) Identification of overlapping communities and their hierarchy by locally calculating community-changing resolution levels. J Stat Mech Theory Exp 2011(01):P01023CrossRefGoogle Scholar
  27. 27.
    Xie J, Szymanski BK (2012) Towards linear time overlapping community detection in social networks. In: Advances in knowledge discovery and data mining, Springer, pp 25–36Google Scholar
  28. 28.
    Dickinson B, Valyou B, Hu W (2013) A genetic algorithm for identifying overlapping communities in social networks using an optimized search space. Soc Networks:2013Google Scholar
  29. 29.
    Mu C, Liu Y, Liu Y, Wu J, Jiao L (2014) Two-stage algorithm using influence coefficient for detecting the hierarchical, non-overlapping and overlapping community structure. Physica A: Statistical Mechanics and its Applications 408:47–61MathSciNetCrossRefGoogle Scholar
  30. 30.
    Evans T, Lambiotte R (2009) Line graphs, link partitions, and overlapping communities. Physical Review E 80(1):016105CrossRefGoogle Scholar
  31. 31.
    Pons P, Latapy M (2006) Computing communities in large networks using random walks. J. Graph Algorithms Appl 10(2):191–218MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Deng X, Li G, Dong M (2015) Finding overlapping communities with random walks on line graph and attraction intensity. In: Wireless algorithms, systems, and applications, Springer, pp 94–103Google Scholar
  33. 33.
    Van Dongen S (2014) Graph clustering by flow simulation University of UtrechtGoogle Scholar
  34. 34.
    Yang B, Cheung WK, Liu J (2007) Community mining from signed social networks. IEEE Trans Knowl Data Eng 19(10):1333–1348CrossRefGoogle Scholar
  35. 35.
    Steinhaeuser K, Chawla NV (2010) Identifying and evaluating community structure in complex networks. Pattern Recognit Lett 31(5):413–421CrossRefGoogle Scholar
  36. 36.
    Lancichinetti A, Fortunato S, Radicchi F (2008) Benchmark graphs for testing community detection algorithms. PHYSICAL REVIEW E 78(4,2)Google Scholar
  37. 37.
    Lancichinetti A, Fortunato S (2009) Benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities. PHYSICAL REVIEW E 80(1,2)Google Scholar
  38. 38.
    Danon L, Diaz-Guilera A, Duch J, Arenas A (2005) Comparing community structure identification. JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENTGoogle Scholar
  39. 39.
    Zachary WW (1977) An information flow model for conflict and fission in small groups. J Anthropol Res:452–473Google Scholar
  40. 40.
    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(4):396–405CrossRefGoogle Scholar
  41. 41.
    Jin D, Yang B, Baquero C, Liu D, He D, Liu J (2011) A markov random walk under constraint for discovering overlapping communities in complex networks. J Stat Mech Theory Exp 2011(05):P05031CrossRefGoogle Scholar
  42. 42.
    Shen H, Cheng X, Cai K, Hu MB (2009) Detect overlapping and hierarchical community structure in networks. Physica A: Statistical Mechanics and its Applications 388(8):1706–1712CrossRefGoogle Scholar
  43. 43.
    Newman ME (2004) Fast algorithm for detecting community structure in networks. Physical review E 69(6):066133CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Xiaoheng Deng
    • 1
  • Genghao Li
    • 1
  • Mianxiong Dong
    • 2
  • Kaoru Ota
    • 2
  1. 1.School of Information Science & EngineeringCentral South UniversityChangshaChina
  2. 2.Department of Information and Electronic EngineeringMuroran Institute of TechnologyMuroranJapan

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