Soft Computing

, Volume 22, Issue 8, pp 2583–2601 | Cite as

A novel subgraph \(K^{+}\)-isomorphism method in social network based on graph similarity detection

  • Huan Rong
  • Tinghuai Ma
  • Meili Tang
  • Jie Cao
Methodologies and Application


In this paper, we propose a novel \(K^{+}\)-isomorphism method to achieve K-anonymization state among subgraphs or detected communities in a given social network. Our proposed \(K^{+}\)-isomorphism method firstly partitions the subgraphs we have detected into some similar-subgraph clusters followed by graph modification conducted in every cluster. In this way, it is feasible to publish preserved structures of communities or subgraphs and every preserved structure actually represents a cluster of at least K subgraphs or communities which are isomorphic to each other. The contributions of this paper are listed as follows: On the one hand, we improve a maximum common subgraph detection algorithm, MPD\(_{-}\)V, which is a core technique for graph similarity detection involved in partition phase of our proposed \(K^{+}\)-isomorphism method; on the other hand, with minor adjustment, we utilize some current techniques as an innovative combination to finish the partition and modification of similar-community cluster in \(K^{+}\)-isomorphism method. The experiments have shown that the improved MPD\(_{-}\)V method has much better efficiency to search larger common subgraphs with acceptable performance compared with its prototype and other techniques. Moreover, our proposed \(K^{+}\)-isomorphism method can achieve the K-isomorphism state with less modification of original network structure, or lower anonymization cost compared to the current K-isomorphism method.


Social network Subgraph similarity detection Subgraph K-anonymization Privacy preservation Maximum common subgraph 



This work was supported in part by National Science Foundation of China (No. 61572259), Special Public Sector Research Program of China (No. GYHY201506080), and was also supported by PAPD.

Compliance with ethical standards

Conflict of interest

Tinghui Ma has received research Grants from National Science Foundation of China and Special Public Sector Research Program of China.

Informed consent

Informed consent was obtained from all individual participants included in the study.


  1. Bhagat S, Cormode G, Krishnamurthy B, Srivastava D (2010) Prediction promotes privacy in dynamic social networks. In: Proceedings of the 3rd conference on online social networks, pp 6–6Google Scholar
  2. Bin G, Sheng VS, Wang Z, Ho D, Osman S, Li S (2015a) Incremental learning for v-support vector regression. Neural Netw 67:140–150CrossRefGoogle Scholar
  3. Bin G, Sheng VS, Tay KY, Romano W, Li S (2015b) Incremental support vector learning for ordinal regression. IEEE Trans Neural Netw Learn Syst 26(7):1403–1416MathSciNetCrossRefGoogle Scholar
  4. Bunke H, Shearer K (1998) A graph distance metric based on the maximal common subgraph. Pattern Recognit Lett 19(3–4):255–259CrossRefzbMATHGoogle Scholar
  5. Casas-Roma J, Herrera-Joancomart J, Torra V (2014) Anonymizing graphs: measuring quality for clustering. Knowl Inf Syst 44(3):507–528CrossRefGoogle Scholar
  6. Chakravorty A, Wlodarczyk TW, Rong C (2014) A scalable K-anonymization solution for preserving privacy in an aging-in-place welfare intercloud. IEEE international conference on cloud engineering. IEEE, pp 424–431Google Scholar
  7. Chen B, Shu H, Coatrieux G, Chen G, Sun X, Coatrieux J-L (2015) Color image analysis by quaternion-type moments. J Math Imaging Vis 51(1):124–144MathSciNetCrossRefzbMATHGoogle Scholar
  8. Cheng J, Fu W C, Liu J (2010) K-isomorphism: privacy preserving network publication against structural attacks. In: ACM SIGMOD international conference on management of data, SIGMOD 2010, Indianapolis, Indiana, USA, June, pp 459–470Google Scholar
  9. Doka K, Xue M, Tsoumakos D et al (2015) k-Anonymization by freeform generalization. In: ACM symposium on information, computer and communications security. ACM, pp 519–530Google Scholar
  10. Eustace J, Wang X (2015) Overlapping community detection using neighborhood ratio matrix. Phys A 421:510–521CrossRefGoogle Scholar
  11. Girvan M, Newman MEJ (2002) Community structure in social and biological networks. Proc Natl Acad Sci 99(12):7821–7826MathSciNetCrossRefzbMATHGoogle Scholar
  12. Gouda K, Hassaan M (2012) A fast algorithm for subgraph search problem. In: 2012 8th international conference on informatics and systems (INFOS). IEEE, pp DE-53–DE-59Google Scholar
  13. Guo P, Wang J, Li B, Lee S (2014) A variable threshold-value authentication architecture for wireless mesh networks. J Internet Technol 15(6):929–936Google Scholar
  14. Guoting F, Yonglong L, Dandan S, Taochun W, Xiaoyao Z (2016) Edge partitioning approach for protecting sensitive relationships in social network. J Comput Appl 36(1):207–211Google Scholar
  15. Huda MN, Yamada S, Sonehara N (2013) An efficient k-anonymization algorithm with low information loss. Lect Notes Electr Eng 156:249–254CrossRefGoogle Scholar
  16. Hu H, Li G, Feng J (2013) Fast similar subgraph search with maximum common connected subgraph constraints. In: IEEE International Congress on big data, pp 181–188Google Scholar
  17. Jiang J, Tan Z, Zhao N et al (2010) MultiMarker propagation Web log mining algorithms based on weighted matrix cluster. In: 2010 2nd international conference on future computer and communication (ICFCC). IEEE, pp V2-374–V2-378Google Scholar
  18. Kiyomoto S, Miyake Y (2014) How to find an appropriate K for K-anonymization. In: 2014 eighth international conference on innovative mobile and Internet services in ubiquitous computing (IMIS). IEEE, pp 273–279Google Scholar
  19. Kuo JJ, Chang JS, Zhang YJ (2013) Visualized book recommender system using matrix clustering. J Educ Media Libr Sci 51(1):5–35Google Scholar
  20. Li J, Wang X (2014) Uncovering the overlapping community structure of complex networks by maximal cliques. Phys A 415:398–406MathSciNetCrossRefGoogle Scholar
  21. Liu X, Yang X (2011) A generalization based approach for anonymizing weighted social network graphs. In: International conference on web-age information management. Springer, Berlin, pp 118–130Google Scholar
  22. Lv Y, Ma T, Tang M et al (2016) An efficient and scalable density-based clustering algorithm for datasets with complex structures. Neurocomputing 171:9–22CrossRefGoogle Scholar
  23. Ma T, Zhang Y, Cao J et al (2015a) KDVEM: a k-degree anonymity with vertex and edge modification algorithm. Computing 97(12):1165–1184MathSciNetCrossRefzbMATHGoogle Scholar
  24. Ma T, Zhou J, Tang M, Tian Y, Al-Dhelaan A, Al-Rodhaan M, Lee S (2015b) Social network and tag sources based augmenting collaborative recommender system. IEICE Trans 98(D(4)):902–910CrossRefGoogle Scholar
  25. Ma T, Wang Y, Tang M et al (2016a) LED: a fast overlapping communities detection algorithm based on structural clustering. Neurocomputing 207:488–500Google Scholar
  26. Ma T, Rong H, Ying C, Tian Y, Al-Dhelaan A, Al-Rodhaan M (2016b) Detect structural-connected communities based on BSCHEF in C-DBLP. Concurr Comput Pract Exp 28(2):311–330CrossRefGoogle Scholar
  27. Madeira SC, Oliveira AL (2004) Biclustering algorithms for biological data analysis: a survey. IEEE ACM Trans Comput Biol Bioinform 1(1):24–45CrossRefGoogle Scholar
  28. Mallek S, Boukhris I, Elouedi Z (2015) Community detection for graph-based similarity: application to protein binding pockets classification. Pattern Recognit Lett 62:49–54CrossRefGoogle Scholar
  29. Mcgregor JJ (1982) Backtrack search algorithms and the maximal common subgraph problem. Softw Pract Exp 12(1):23–34CrossRefzbMATHGoogle Scholar
  30. Okada R, Watanabe C, Kitagawa H (2014) A k-Anonymization algorithm on social network data that reduces distances between nodes. In: Proceedings of the 2014 IEEE 33rd international symposium on reliable distributed systems workshops. IEEE Computer Society, pp 76–81Google Scholar
  31. Praveena A, Smys S (2016) Anonymization in social networks: a survey on the issues of data privacy in social network sites. Int J Eng Comput Sci 5(3):15912–15918CrossRefGoogle Scholar
  32. Rajaei M, Haghjoo MS, Miyaneh EK (2015) Ambiguity in social network data for presence, sensitive-attribute, degree and relationship privacy protection. PLoS ONE 10(6):e0130693Google Scholar
  33. Raymond JW, Willett P (2002) Maximum common subgraph isomorphism algorithms for the matching of chemical structures. J Comput Aided Mol Des 16(7):521–533CrossRefGoogle Scholar
  34. Ullmann JR (1976) An algorithm for subgraph isomorphism. J ACM 23(23):31–42MathSciNetCrossRefGoogle Scholar
  35. Wang Y, Maple C (2005) A novel efficient algorithm for determining maximum common subgraphs. In: International conference on information visualisation. IEEE Computer Society, pp 657–663Google Scholar
  36. Wang Y, Xie L, Zheng B et al (2014) High utility K-anonymization for social network publishing. Knowl Inf Syst 41(3):697–725CrossRefGoogle Scholar
  37. Wen X, Shao L, Xue Y, Wei F (2015) A rapid learning algorithm for vehicle classification. Inf Sci 295(1):395–406CrossRefGoogle Scholar
  38. Wu W, Xiao Y, Wang W et al (2010) k-symmetry model for identity anonymization in social networks. In: International conference on extending database technology. ACM, pp 111–122Google Scholar
  39. Xie Y, Zheng M, Liu L (2016) A personalized sensitive label-preserving model and algorithm based on utility in social network data publishing. LNCS 9567:1–11Google Scholar
  40. Xu X, Numao M (2015) An efficient generalized clustering method for achieving K-anonymization. In: Third international symposium on computing and networking. IEEE Computer Society, pp 499–502Google Scholar
  41. Yang J, Wang B, Yang X et al (2014) A secure K-automorphism privacy preserving approach with high data utility in social networks. Secur Commun Netw 7(9):1399–1411CrossRefGoogle Scholar
  42. Zaghian A, Bagheri A (2016) A combined model of clustering and classification methods for preserving privacy in social networks against inference and neighborhood attacks. Int J Secur Appl 10(1):95–102Google Scholar
  43. Zhang ZY, Li T, Ding C et al (2010) Binary matrix factorization for analyzing gene expression data. Data Min Knowl Discov 20(1):28–52MathSciNetCrossRefGoogle Scholar
  44. Zhang XL, Tang Y (2014) Protecting encrypted data against inference attacks in outsourced databases. Appl Mech Mater 571–572:621–625Google Scholar
  45. Zheng Y, Jeon B, Danhua X, Jonathan Wu QM, Zhang H (2015) Image segmentation by generalized hierarchical fuzzy C-means algorithm. J Intell Fuzzy Syst 28(2):961–973Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.School of ComputerNanjing University of Information Science and TechnologyNanjingChina
  2. 2.CICAEET, Jiangsu Engineering Centre of Network MonitoringNanjing University of Information Science and TechnologyNanjingChina
  3. 3.School of Public AdministrationNanjing University of Information Science and TechnologyNanjingChina
  4. 4.School of Economics and ManagementNanjing University of Information Science and TechnologyNanjingChina

Personalised recommendations