Skip to main content
SpringerLink
Log in

Link prediction in complex network based on modularity

  • Focus
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

The problem of link prediction has attracted considerable recent attention from various domains such as sociology, anthropology, information science, and computer sciences. A link prediction algorithm is proposed using the modularity measure reflecting the community structure information of the network. Based on the fact that the connection likelihood between a pair of nodes in the same community is larger than those separated in different communities, we propose a new measure, named modularity contribution, for predicting link between a pair of nodes using information from intra-community and within-community of these nodes. Using the modularity contribution, we map the nodes to an Euclidean space. In this space, the nodes trending to be included in the same community are closely located. The cosine similarity of the nodes in this space is used in computing the similarity measure for link prediction. We also extend the method to solve the link prediction on networks of nodes with attributes. Our experimental results show that the proposed algorithm can obtain higher quality results than other algorithms.

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

Similar content being viewed by others

References

  • Ahn MW, Jung WS (2015) Accuracy test for link prediction in terms of similarity index: the case of WS and BA models. Physica A: Stat Mech Appl 429(1):177–183

    Article  Google Scholar 

  • Aiello LM, Barrat A, Schifanella R et al (2012) Friendship prediction and homophily in social media. ACM Trans Web 6(2):9

  • Almohammadi K, Hagras H, Yao B, Alzahrani A (2015) A type-2 fuzzy logic recommendation system for adaptive teaching. Soft Comput. doi:10.1007/s00500-015-1826-y

  • Backstrom J, Leskovec J (2011) Supervised random walks: predicting and recommending links in social networks. In: Proceedings of WSDM 2011

  • Bao ZF, Zeng Y, Tay YC (2013) sonLP: social network link prediction by principal component regression. In: Proceedings of the 2013 IEEE/ACM international conference on advances in social networks analysis and mining

  • Barbieri N, Bonchi F, Manco G (2014) Who to follow and why: link prediction with explanations. In: Proceedings of the 20th ACM SIGKDD international conference on knowledge discovery and data mining, pp 1266–1275

  • Bliss CA, Frank MR, Danfo CM, Dodds PS (2014) An evolutionary algorithm approach to link prediction in dynamic social networks. J Comput Sci 5(5):750–764

    Article  MathSciNet  Google Scholar 

  • Borchers B (1999) CSDP: a C library for semidefinite programming. Optim Methods Softw 11:613–623

    Article  MathSciNet  MATH  Google Scholar 

  • Bouziane H, Messabih B, Chouarfia A (2015) Effect of simple ensemble methods on protein secondary structure prediction. Soft Comput 19:1663–1678

    Article  Google Scholar 

  • Bringmann B, Berlingerio M, Bonchi F, Gionis A (2010) Learning and predicting the evolution of social networks. IEEE Intell Syst 25(4):26–34

    Article  Google Scholar 

  • Buccafurri F, Lax G, Nocera A, Ursino D (2015) Discovering missing me edges across social networks. Inf Sci 319:18–37

    Article  MathSciNet  Google Scholar 

  • Ding JY, Jiao LC, Wu JS, Hou YT, Qi YT (2015) Prediction of missing links based on multi-resolution community division. Physica A: Stat Mech Appl 417(1):76–85

    Article  Google Scholar 

  • Fang H, Xu L, Huang XY (2015) Self-adaptive trust management based on game theory in fuzzy large-scale networks. Soft Comput. doi:10.1007/s00500-015-1821-3

  • Feng X, Zhao JC, Xu K (2012) Link prediction in complex networks: a clustering perspective. Eur Phys J B 85(3):1–9

    Google Scholar 

  • Fournet J, Barrat A (2014) Contact patterns among high school students. PLoS One 9(8):e107878

    Article  Google Scholar 

  • Gao S, Denoyer L, Gallinari P et al (2012) Probabilistic latent tensor factorization model for link pattern prediction in multi-relational networks. J China Univ Posts Telecommun 19:172–181

    Article  Google Scholar 

  • Gao S, Denoyer L, Gallinari P (2011) Temporal link prediction by integrating content and structure information. In: Proceedings of CIKM’11, Glasgow, Scotland, UK, pp 1169–1174

  • Golub G, Van Loan C (1983) Matrix computations. The Johns Hopkins University Press, Baltimore

  • Guimera R, Sales-Pardo M (2010) Missing and spurious interactions and the reconstruction of complex networks. Proc Natl Acad Sci USA 106(52):22073–22078

    Article  Google Scholar 

  • Guo L, Ma J, Chen ZM, Zhong H (2015) Learning to recommend with social contextual information from implicit feedback. Soft Comput 19:1351–1362

    Article  Google Scholar 

  • Hanneke S, Fu WJ, Xing EP (2010) Discrete temporal models of social networks. Electron J Stat 4:585–605

    Article  MathSciNet  MATH  Google Scholar 

  • He YL, Liu JNK, Hu YX, Wang XZ (2015) OWA operator based link prediction ensemble for social network. Expert Syst Appl 42(1):21–50

    Article  Google Scholar 

  • Hoffman M, Steinley D, Brusco MJ (2015) A note on using the adjusted Rand index for link prediction in networks. Soc Netw 42:72–79

    Article  Google Scholar 

  • Huang Z, Lin DKJ (2009) The time-series link prediction problem with applications in communication surveillance. INFORMS J Comput 21:286–303

    Article  Google Scholar 

  • Hu FY, Wong HS (2013) Labeling of human motion based on CBGA and probabilistic model. Int J Smart Sens Intell Syst 6(2):583–609

    Google Scholar 

  • Ibrahim NMA, Chen L (2015) Link prediction in dynamic social networks by integrating different types of information. Appl Intell 42(4):738–750

    Article  Google Scholar 

  • Jorge Carlos VR, de Andrade Lopes A (2012) Structural link prediction using community information on Twitter. In: Proceedings of the 2012 Fourth International Conference on Computational Aspects of Social Networks (CASoN). IEEE Publisher, Sao Carlos, Brazil, pp 132–137

  • Kaya B, Poyraz M (2014) Supervised link prediction in symptom networks with evolving case. Measurement 56:231–238

    Article  Google Scholar 

  • Kaya B, Poyraz M (2015) Age-series based link prediction in evolving disease networks. Comput Biol Med 63:1–10

    Article  Google Scholar 

  • Latora V, Marchiori M (2001) Efficient behavior of small-world networks. Phys Rev Lett 67:198701–198704

    Article  Google Scholar 

  • Li J, Zhang LL, Meng F, Li FH (2014) Recommendation algorithm based on link prediction and domain knowledge in retail transactions. Procedia Comput Sci 31:875–881

    Article  Google Scholar 

  • Liao H, Zeng A, ZhangY C (2015) Predicting missing links via correlation between nodes. Physica A: Stat Mech Appl 436:216–223

  • Li X, Chen HC (2013) Recommendation as link prediction in bipartite graphs: a graph kernel-based machine learning approach. Decis Support Syst 54(2):880–890

    Article  Google Scholar 

  • Lichtenwalter RN (2010) New precepts and method in link prediction. In: Proceedings of ACM KDD’10, pp 243–252

  • Liu HK, Lü LY, Zhou T (2011) Uncovering the network evolution mechanism by link prediction (in Chinese). Sci Sin Phys Mech Astron 41:816–823

    Article  Google Scholar 

  • Liu J, Denga G (2009) Link prediction in a user-object network based on time-weighted resource allocation. Physica A 388:3643–3650

    Article  Google Scholar 

  • Liu WP, Lü L (2010) Link prediction based on local random walk. Eur Phys Lett 89(5):58007

    Article  Google Scholar 

  • Lü LY, Jin CH, Zhou T (2009) Similarity index based on local paths for link prediction of complex networks. Phys Rev E Stat Nonlinear Soft Matter Phys 80(4):046122

    Article  Google Scholar 

  • Lü LY, Zhou T (2011) Link prediction in complex networks: a survey. Physica A 390:1150–1170

    Article  Google Scholar 

  • Ma X, Liao JL, Djouadi SM, Cao Q (2014) LIPS: link prediction as a service for data aggregation applications. Ad Hoc Netw 19:43–58

    Article  Google Scholar 

  • Menon AK, Elkan C (2011) Link prediction via matrix factorization. In Proceedings of ECML/PKDD, 2011

  • Miller KT, Griffiths TL, Jordan MI (2009) Nonparametric latent feature models for link prediction. In: NIPS, 2009

  • Newman MEJ (2002) Assortative mixing in networks. Phys Rev Lett 89:208701–208705

    Article  Google Scholar 

  • Nilashi M, Ibrahim OB, Ithnin N, Zakaria R (2015) A multi-criteria recommendation system using dimensionality reduction and Neuro-Fuzzy techniques. Soft Comput 19:3173–3207

    Article  Google Scholar 

  • Popescul A, Ungar L (2003) Statistical relational learning for link prediction. In: Proceedings of the international workshop on learning statistical models from relational data, Acapulco, Mexico, vol. 149, pp 172–179

  • Pujari M, Kanawati R (2012) Supervised rank aggregation approach for link prediction in complex networks. In: Proceedings of WWW 2012 Companion. Lyon, France, pp 1189–1196

  • Scripps J, Tan PN, Chen F, Esfahanian AH (2009) A matrix alignment approach for collective classification. In: Proceedings of ASONAM 2009, Athens, Greece

  • Sherkat E, Rahgozar M, Asadpour M (2015) Structural link prediction based on ant colony approach in social networks. Physica A: Stat Mech Appl 419(1):80–94

    Article  Google Scholar 

  • Soundarajan S, Hopcroft JH (2012) Using community information to improve the precision of link prediction methods. WWW (Companion Volume) 2012:607–608

    Google Scholar 

  • Sun Y, Barbery R, Gupta M, Aggarwal CC, Han J (2011) Co-author relationship prediction in heterogeneous bibliographic networks. In: Proceedings of 2011 international conference on advances in social networks analysis and mining, ASONAM 2011, pp 121–128

  • Taskar B, Wong MF, Abbeel P, Koller D (2003) Link prediction in relational data. In: NIPS, 2003

  • Vidmer A, Zeng A, Medo M, Zhang YC (2015) Prediction in complex systems: the case of the international trade network. Physica A: Stat Mech Appl 436:188–199

    Article  Google Scholar 

  • Vu DQ, Asuncion AU, Hunter DR, Smyth P (2011) Continuous-time regression models for longitudinal networks. Advances in neural information processing systems 24: Proceedings of the 25th annual conference on neural information processing systems, pp 1–9

  • Wang XJ, Zhang X, Zhao CL, Xie Z, Zhang SJ, Yi DY (2015) Predicting link directions using local directed path. Physica A Stat Mech Appl 419:260–267

    Article  Google Scholar 

  • Wang M, Ma J (2015) A novel recommendation approach based on users’ weighted trust relations and the rating similarities. Soft Comput. doi:10.1007/s00500-015-1734-1

  • Watts DJ, Strogatz S (1998) Collective dynamics of ‘small-world’ networks. Nature 393(6684):440–442

    Article  Google Scholar 

  • Wei J, Zeng QF, Wang X, Wang JB, Wen GH (2014) Integrating local and global topological structures for semi-supervised dimensionality reduction. Soft Comput 18:1189–1198

    Article  Google Scholar 

  • Xie F, Chen Z, Shang JX, Feng XP, Li J (2015) A link prediction approach for item recommendation with complex number. Knowl Based Syst 81:148–158

    Article  Google Scholar 

  • Yin Z, Gupta M, Weninger T, Han J (2010) Linkrec: a unified framework for link recommendation with user attributes and graph structure. In: Proceedings of WWW, 2010

  • Zeng ZZ, Chen KJ, Zhang SB, Zhang HJ (2013) A link prediction approach using semi-supervised learning in dynamic networks. In: Proceedings of 6th international conference on advanced computational intelligence (ICACI), pp 276–280

  • Zhang L, Hu K, Tang Y (2010) Predicting disease-related genes by topological similarity in human protein–protein interaction network. Cent Eur J Phys 8(4):672–682

    Google Scholar 

  • Zhou T, Lü L, Zhang YC (2009) Predicting missing links via local information. Eur Phys J B 71(4):623–630

    Article  MATH  Google Scholar 

Download references

Acknowledgments

This research was supported in part by the Chinese National Natural Science Foundation under Grant Nos. 61379066, 61070047, 61379064, 61472344, Natural Science Foundation of Jiangsu Province under contracts BK20130452, BK2012672, BK2012128, and Natural Science Foundation of Education Department of Jiangsu Province under contracts 12KJB520019, 13KJB520026, 09KJB20013. Six talent peaks project in Jiangsu Province (Grant No. 2011-DZXX-032).

Author information

Authors and Affiliations

  1. College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Dai Caiyan

  2. Department of Computer Science, Yangzhou University, Yangzhou, 225127, China

    Ling Chen & Bin Li

  3. State Key Lab of Novel Software Tech, Nanjing University, Nanjing, 210093, China

    Ling Chen & Bin Li

Authors
  1. Dai Caiyan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ling Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bin Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ling Chen.

Ethics declarations

Conflict of interest

We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.

Additional information

Communicated by W.-Y. Lin, H.-C. Yang, T.-P. Hong and L.S.L. Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Caiyan, D., Chen, L. & Li, B. Link prediction in complex network based on modularity. Soft Comput 21, 4197–4214 (2017). https://doi.org/10.1007/s00500-016-2030-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-016-2030-4

Keywords

Search

Navigation