Skip to main content
SpringerLink
Log in

Community detection in attributed networks considering both structural and attribute similarities: two mathematical programming approaches

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

Community detection is one of the most well-known and emerging research topics in the area of social network analysis. There are a wide variety of approaches to find communities in the literature, each with its own advantages and disadvantages. A majority of these approaches tend to detect communities by only using the network topology. However, the distribution of the node attributes is correlated with the community structure in many real networks. Therefore, the quality of the discovered partitions can be enhanced by considering node attributes. In this study, two novel mathematical programming approaches are proposed to integrate the topological structure and node similarities, in which first the primary attributed network is converted into a secondary non-attributed network. Then, a mathematical model will be developed to find communities in the secondary network. Thanks to the fact that the objective function and constraints of the proposed model are defined linear, the global optimality of the obtained solutions is guaranteed. In order to validate the proposed approaches, they are applied to both real-world and benchmark networks. Computational results of two well-known evaluation measures including Rand index and normalized mutual information demonstrate the efficiency of the proposed approaches in discovering better partitions.

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. Fortunato S, Hric D (2016) Community detection in networks: a user guide. Phys Rep 659:1–44

    MathSciNet  Google Scholar 

  2. Beiró MG, Busch JR, Grynberg SP, Alvarez-Hamelin JI (2013) Obtaining communities with a fitness growth process. Physica A 392:2278–2293

    Google Scholar 

  3. Fortunato S (2010) Community detection in graphs. Phys Rep 486:75–174

    MathSciNet  Google Scholar 

  4. Girvan M, Newman ME (2002) Community structure in social and biological networks. Proc Natl Acad Sci 99:7821–7826

    MathSciNet  MATH  Google Scholar 

  5. Newman MEJ (2016) Equivalence between modularity optimization and maximum likelihood methods for community detection. Phys Rev E 94:052315

    Google Scholar 

  6. Xu G, Tsoka S, Papageorgiou LG (2007) Finding community structures in complex networks using mixed integer optimisation. Eur Phys J B 60:231–239

    MATH  Google Scholar 

  7. Hric D, Darst RK, Fortunato S (2014) Community detection in networks: structural communities versus ground truth. Phys Rev E 90:062805

    Google Scholar 

  8. Leskovec J, Mcauley JJ (2012) Learning to discover social circles in ego networks. In: Pereira F, Burges CJC, Bottou L, Weinberger KQ (eds) Advances in neural information processing systems. Curran Associates Inc, New York, pp 539–547

    Google Scholar 

  9. Zhang Y, Levina E, Zhu J (2016) Community detection in networks with node features. Electron J Stat 10:3153–3178

    MathSciNet  MATH  Google Scholar 

  10. Li Y, Wang H, Li J, Gao H (2013) Efficient community detection with additive constrains on large networks. Knowl Based Syst 52:268–278

    Google Scholar 

  11. De Meo P, Ferrara E, Fiumara G, Provetti A (2013) Enhancing community detection using a network weighting strategy. Inf Sci 222:648–668

    MathSciNet  MATH  Google Scholar 

  12. Duan L, Liu Y, Nick Street W, Lu H (2017) Utilizing advances in correlation analysis for community structure detection. Expert Syst Appl 84:74–91

    Google Scholar 

  13. Costa A, Ng TS, Foo LX (2017) Complete mixed integer linear programming formulations for modularity density based clustering. Discrete Optim 25:141–158

    MathSciNet  MATH  Google Scholar 

  14. Francisquini R, Rosset V, Nascimento MCV (2017) GA-LP: a genetic algorithm based on label propagation to detect communities in directed networks. Expert Syst Appl 74:127–138

    Google Scholar 

  15. Guerrero M, Montoya FG, Baños R et al (2017) Adaptive community detection in complex networks using genetic algorithms. Neurocomputing 266:101–113

    Google Scholar 

  16. Li Z, Wang R-S, Zhang S, Zhang X-S (2016) Quantitative function and algorithm for community detection in bipartite networks. Inf Sci 367:874–889

    MATH  Google Scholar 

  17. Peel L, Larremore DB, Clauset A (2017) The ground truth about metadata and community detection in networks. Sci Adv 3:e1602548

    Google Scholar 

  18. Rocco CM, Moronta J, Ramirez-Marquez JE, Barker K (2017) Effects of multi-state links in network community detection. Reliab Eng Syst Saf 163:46–56

    Google Scholar 

  19. Staudt CL, Meyerhenke H (2016) Engineering parallel algorithms for community detection in massive networks. IEEE Trans Parallel Distrib Syst 27:171–184

    Google Scholar 

  20. Žalik KR, Žalik B (2018) Multi-objective evolutionary algorithm using problem-specific genetic operators for community detection in networks. Neural Comput Appl 30(9):2907–2920

    Google Scholar 

  21. Papadopoulos S, Kompatsiaris Y, Vakali A, Spyridonos P (2012) Community detection in social media. Data Min Knowl Disc 24:515–554

    Google Scholar 

  22. Yang B, Liu D, Liu J (2010) Discovering communities from social networks: methodologies and applications. In: Furht B (ed) Handbook of social network technologies and applications. Springer, New York, pp 331–346

    Google Scholar 

  23. Bindu PV, Thilagam PS, Ahuja D (2017) Discovering suspicious behavior in multilayer social networks. Comput Hum Behav 73:568–582

    Google Scholar 

  24. Interdonato R, Tagarelli A, Ienco D et al (2017) Node-centric community detection in multilayer networks with layer-coverage diversification bias. In: Gonçalves B, Menezes R, Sinatra R, Zlatic V (eds) Complex networks VIII. CompleNet 2017. Springer proceedings in complexity. Springer, Cham, pp 57–66

  25. Interdonato R, Tagarelli A, Ienco D et al (2016) Local community detection in multilayer networks. In: 2016 IEEE/ACM international conference on advances in social networks analysis and mining (ASONAM), pp 1382–1383

  26. Jeub LGS, Mahoney MW, Mucha PJ, Porter MA (2017) A local perspective on community structure in multilayer networks. Netw Sci 5:144–163

    Google Scholar 

  27. Vallès-Català T, Massucci FA, Guimerà R, Sales-Pardo M (2016) Multilayer stochastic block models reveal the multilayer structure of complex networks. Phys Rev X 6:011036

    Google Scholar 

  28. Chen Y, Wang X, Bu J et al (2016) Network structure exploration in networks with node attributes. Physica A 449:240–253

    MathSciNet  MATH  Google Scholar 

  29. Du H, Sun H, Huang J et al (2017) Mining cohesive clusters with interpretations in labeled graphs. In: Kim J, Shim K, Cao L, Lee J-G, Lin X, Moon Y-S (eds) Advances in knowledge discovery and data mining. Springer, Cham, pp 774–785

  30. Gibson H, Vickers P (2016) Using adjacency matrices to lay out larger small-world networks. Appl Soft Comput 42:80–92

    Google Scholar 

  31. Jia C, Li Y, Carson MB et al (2017) Node attribute-enhanced community detection in complex networks. Sci Rep 7:2626

    Google Scholar 

  32. Reihanian A, Feizi-Derakhshi M-R, Aghdasi HS (2017) Community detection in social networks with node attributes based on multi-objective biogeography based optimization. Eng Appl Artif Intell 62:51–67

    Google Scholar 

  33. Levchuk G, Roberts J, Freeman J (2012) Learning and detecting patterns in multi-attributed network data. In: AAAI fall symposium: social networks and social contagion

  34. Mousavi SF, Safayani M, Mirzaei A, Bahonar H (2017) Hierarchical graph embedding in vector space by graph pyramid. Pattern Recogn 61:245–254

    MATH  Google Scholar 

  35. Papadopoulos A, Pallis G, Dikaiakos MD (2013) Identifying clusters with attribute homogeneity and similar connectivity in information networks. In: IEEE, pp 343–350

  36. Bothorel C, Cruz JD, Magnani M, Micenkova B (2015) Clustering attributed graphs: models, measures and methods. Netw Sci 3:408–444

    Google Scholar 

  37. Steinhaeuser K, Chawla NV (2010) Identifying and evaluating community structure in complex networks. Pattern Recogn Lett 31:413–421

    Google Scholar 

  38. Neville J, Adler M, Jensen D (2003) Clustering relational data using attribute and link information. In: Proceedings of the text mining and link analysis workshop, 18th international joint conference on artificial intelligence, pp 9–15

  39. Falih I, Grozavu N, Kanawati R, Bennani Y (2017) ANCA: attributed network clustering algorithm. In: Cherifi C, Cherifi H, Karsai M, Musolesi M (eds) Complex networks and their applications VI. Springer, Cham, pp 241–252

  40. Combe D, Largeron C, Egyed-Zsigmond E, Géry M (2012) Combining relations and text in scientific network clustering. In: 2012 IEEE/ACM international conference on advances in social networks analysis and mining (ASONAM). IEEE, pp 1248–1253

  41. Cheng H, Zhou Y, Yu JX (2011) Clustering large attributed graphs: a balance between structural and attribute similarities. Acm Trans Knowl Discov Data 5:12:1–12:33

    Google Scholar 

  42. Zhou Y, Cheng H, Yu JX (2009) Graph clustering based on structural/attribute similarities. Proc VLDB Endow 2:718–729

    Google Scholar 

  43. Balasubramanyan R, Cohen W (2011) Block-LDA: jointly modeling entity-annotated text and entity-entity links. In: Proceedings of the 2011 SIAM international conference on data mining. Society for Industrial and Applied Mathematics, pp 450–461

  44. Xu Z, Ke Y, Wang Y et al (2012) A model-based approach to attributed graph clustering. In: Proceedings of the 2012 ACM SIGMOD international conference on management of data. ACM, pp 505–516

  45. Xu Z, Cheng J, Xiao X et al (2017) Efficient nonparametric and asymptotic Bayesian model selection methods for attributed graph clustering. Knowl Inf Syst 53:239–268

    Google Scholar 

  46. Wu P, Pan L (2018) Mining application-aware community organization with expanded feature subspaces from concerned attributes in social networks. Knowl Based Syst 139:1–12

    Google Scholar 

  47. Martinez-Seis B (2017) RELNA: ranking attributes in social networks to detect overlapping communities efficiently. In: IEEE, pp 1431–1435

  48. Günnemann S, Boden B, Färber I, Seidl T (2013) Efficient mining of combined subspace and subgraph clusters in graphs with feature vectors. In: Advances in knowledge discovery and data mining. Springer, pp 261–275

  49. Dang TA, Viennet E (2012) Community detection based on structural and attribute similarities. In: International conference on digital society (ICDS), pp 7–12

  50. Blondel VD, Guillaume J-L, Lambiotte R, Lefebvre E (2008) Fast unfolding of communities in large networks. J Stat Mech Theory Exp 2008:P10008

    MATH  Google Scholar 

  51. Ruan Y, Fuhry D, Parthasarathy S (2013) Efficient community detection in large networks using content and links. In: Proceedings of the 22nd international conference on World Wide Web. International World Wide Web conferences steering committee, pp 1089–1098

  52. Sattari M, Zamanifar K (2018) A cascade information diffusion based label propagation algorithm for community detection in dynamic social networks. J Comput Sci 25:122–133

    Google Scholar 

  53. Pool S, Bonchi F, van Leeuwen M (2014) Description-driven community detection. ACM Trans Intell Syst Technol TIST 5:28

    Google Scholar 

  54. Atzmueller M, Doerfel S, Mitzlaff F (2016) Description-oriented community detection using exhaustive subgroup discovery. Inf Sci 329:965–984

    Google Scholar 

  55. Qin M, Jin D, He D et al (2017) Adaptive community detection incorporating topology and content in social networks. ACM Press, New York, pp 675–682

    Google Scholar 

  56. Li Z, Pan Z, Hu G et al (2017) Detecting semantic communities in social networks. IEICE Trans Fundam Electron Commun Comput Sci E100.A:2507–2512

    Google Scholar 

  57. Wang X, Jin D, Cao X et al (2016) Semantic community identification in large attribute networks. In: AAAI, pp 265–271

  58. Yang T, Jin R, Chi Y, Zhu S (2009) Combining link and content for community detection: a discriminative approach. In: Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining. ACM, pp 927–936

  59. Xu G, Bennett L, Papageorgiou LG, Tsoka S (2010) Module detection in complex networks using integer optimisation. Algorithms Mol Biol 5:36

    Google Scholar 

  60. Bennett L, Liu S, Papageorgiou LG, Tsoka S (2012) A mathematical programming approach to community structure detection in complex networks. In: Proceedings of the 22nd European symposium on computer aided process engineering, pp 1387–1391

  61. Bennett L, Liu S, Papageorgiou LG, Tsoka S (2012) Detection of disjoint and overlapping modules in weighted complex networks. Adv Complex Syst 15:1150023

    MathSciNet  Google Scholar 

  62. Lastusilta T, Papageorgiou LG, Westerlund T (2011) A comparative study of solving the problem of module identification in a complex network. Chem Eng 24:319

    Google Scholar 

  63. Agarwal G, Kempe D (2008) Modularity-maximizing graph communities via mathematical programming. Eur Phys J B 66:409–418

    MathSciNet  MATH  Google Scholar 

  64. Nascimento MCV, Pitsoulis L (2013) Community detection by modularity maximization using GRASP with path relinking. Comput Oper Res 40:3121–3131

    MathSciNet  MATH  Google Scholar 

  65. Li W (2013) Revealing network communities with a nonlinear programming method. Inf Sci 229:18–28

    MathSciNet  MATH  Google Scholar 

  66. Bettinelli A, Hansen P, Liberti L (2015) Community detection with the weighted parsimony criterion. J Syst Sci Complex 28:517–545

    MathSciNet  MATH  Google Scholar 

  67. Brandes U, Delling D, Gaertler M et al (2008) On modularity clustering. IEEE Trans Knowl Data Eng 20:172–188

    Google Scholar 

  68. Brandes U, Delling D, Gaertler M et al (2007) On finding graph clusterings with maximum modularity. In: International workshop on graph-theoretic concepts in computer science. Springer, pp 121–132

  69. Chen WYC, Dress AWM, Yu WQ (2008) Community structures of networks. Math Comput Sci 1:441–457

    MathSciNet  MATH  Google Scholar 

  70. Chen WYC, Dress A, Yu WQ (2014) detecting community structures in networks using a linear-programming based approach: a review. In: Pedrycz W, Chen S-M (eds) Social networks: a framework of computational intelligence. Springer, Cham, pp 1–19

    Google Scholar 

  71. Dinh TN, Li X, Thai MT (2015) Network clustering via maximizing modularity: approximation algorithms and theoretical limits. In: 2015 IEEE international conference on data mining (ICDM). IEEE, pp 101–110

  72. Lin C-C, Kang J-R, Chen J-Y (2015) An integer programming approach and visual analysis for detecting hierarchical community structures in social networks. Inf Sci 299:296–311

    Google Scholar 

  73. Li Z, Zhang S, Zhang X (2015) Mathematical model and algorithm for link community detection in bipartite networks. Am J Operations Res 05:421–434

    Google Scholar 

  74. Li Z, Zhang X-S, Wang R-S et al (2013) Discovering link communities in complex networks by an integer programming model and a genetic algorithm. PLoS ONE 8:e83739

    Google Scholar 

  75. Zhu Y, Sun C, Li D et al (2015) Searching graph communities by modularity maximization via convex optimization. In: Combinatorial optimization and applications. Springer, Cham, pp 701–708

  76. Zhu Y, Li D, Xu W et al (2014) Mutual-relationship-based community partitioning for social networks. IEEE Trans Emerg Top Comput 2:436–447

    Google Scholar 

  77. Alguliev RM, Aliguliyev RM, Ganjaliyev FS (2013) Partition clustering-based method for detecting community structures in weighted social networks. Int J Inf Process Manag 4:60–72

    Google Scholar 

  78. Bredin H, Poignant J (2013) Integer linear programming for speaker diarization and cross-modal identification in tv broadcast. In: The 14rd annual conference of the international speech communication association, INTERSPEECH

  79. Figueiredo R, Moura G (2013) Mixed integer programming formulations for clustering problems related to structural balance. Soc Netw 35:639–651

    Google Scholar 

  80. Heo S, Daoutidis P (2016) Control-relevant decomposition of process networks via optimization-based hierarchical clustering. AIChE J 62:3177–3188

    Google Scholar 

  81. Levorato M, Figueiredo R, Frota Y, Drummond L (2017) Evaluating balancing on social networks through the efficient solution of correlation clustering problems. EURO J Comput Optim 5:467–498

    MathSciNet  MATH  Google Scholar 

  82. Bhimani J, Mi N, Leeser M, Yang Z (2017) FiM: performance prediction for parallel computation in iterative data processing applications. In: 2017 IEEE 10th international conference on cloud computing (CLOUD). IEEE, pp 359–366

  83. Yang Z, Wang Y, Bhamini J et al (2018) EAD: elasticity aware deduplication manager for datacenters with multi-tier storage systems. Clust Comput 21(3):1561–1579

    Google Scholar 

  84. Bhimani J, Yang Z, Leeser M, Mi N (2017) Accelerating big data applications using lightweight virtualization framework on enterprise cloud. In: 2017 IEEE high performance extreme computing conference (HPEC). IEEE, pp 1–7

  85. Bhimani J, Yang Z, Mi N et al (2018) Docker container scheduler for I/O intensive applications running on NVMe SSDs. IEEE Trans Multi Scale Comput Syst 4(3):313–326

    Google Scholar 

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

    Google Scholar 

  87. Lusseau D (2003) The emergent properties of a dolphin social network. Proc R Soc Lond B Biol Sci 270:S186–S188

    Google Scholar 

  88. Craven M, DiPasquo D, Freitag D et al (1998) Learning to extract symbolic knowledge from the World Wide Web. In: Proceedings of the fifteenth national/tenth conference on artificial intelligence/innovative applications of artificial intelligence. American Association for Artificial Intelligence, Menlo Park, pp 509–516

  89. Tang L, Wang X, Liu H (2012) Community detection via heterogeneous interaction analysis. Data Min Knowl Disc 25:1–33

    MathSciNet  Google Scholar 

  90. Rand WM (1971) Objective criteria for the evaluation of clustering methods. J Am Stat Assoc 66:846–850

    Google Scholar 

  91. Witten IH, Frank E (2005) Data mining, fourth edition: practical machine learning tools and techniques, 4th edn. Morgan Kaufmann, Amsterdam

    MATH  Google Scholar 

  92. Pizzuti C (2017) Evolutionary computation for community detection in networks: a review. IEEE Transact Evol Comput 22:464–483

    Google Scholar 

  93. Liu X, Wang W, He D et al (2017) Semi-supervised community detection based on non-negative matrix factorization with node popularity. Inf Sci 381:304–321

    Google Scholar 

  94. McDaid AF, Greene D, Hurley N (2011) Normalized mutual information to evaluate overlapping community finding algorithms. arXiv:11102515

  95. Harenberg S, Bello G, Gjeltema L et al (2014) Community detection in large-scale networks: a survey and empirical evaluation: community detection in large-scale networks. Wiley Interdiscip Rev Comput Stat 6:426–439

    Google Scholar 

  96. Tan P-N, Steinbach M, Kumar V (2006) Introduction to data mining. Pearson Addison Wesley, Boston

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Industrial and Systems Engineering, Tarbiat Modares University, P.O. Box 14115-143, Room 210, Tehran, Iran

    Esmaeil Alinezhad, Babak Teimourpour, Mohammad Mehdi Sepehri & Mehrdad Kargari

Authors
  1. Esmaeil Alinezhad
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Babak Teimourpour
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mohammad Mehdi Sepehri
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mehrdad Kargari
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Babak Teimourpour.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

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

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Alinezhad, E., Teimourpour, B., Sepehri, M.M. et al. Community detection in attributed networks considering both structural and attribute similarities: two mathematical programming approaches. Neural Comput & Applic 32, 3203–3220 (2020). https://doi.org/10.1007/s00521-019-04064-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-019-04064-5

Keywords

Search

Navigation