Skip to main content

Effective k-Vertex Connected Component Detection in Large-Scale Networks

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 10178))

Abstract

Finding components with high connectivity is an important problem in component detection with a wide range of applications, e.g., social network analysis, web-page research and bioinformatics. In particular, k-edge connected component (k-ECC) has recently been extensively studied to discover disjoint components. Yet many real applications present needs and challenges for overlapping components. In this paper, we propose a k-vertex connected component (k-VCC) model, which is much more cohesive and therefore allows overlapping between components. To find k-VCCs, a top-down framework is first developed to find the exact k-VCCs. To further reduce the high computational cost for input networks of large sizes, a bottom-up framework is then proposed. Instead of using the structure of the entire network, it locally identifies the seed subgraphs, and obtains the heuristic k-VCCs by expanding and merging these seed subgraphs. Comprehensive experimental results on large real and synthetic networks demonstrate the efficiency and effectiveness of our approaches.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    thebiogrid.org.

  2. 2.

    http://snap.standford.edu.

  3. 3.

    http://dblp.uni-trier.de/xml/.

References

  1. Akiba, T., Iwata, Y., Yoshida, Y.: Linear-time enumeration of maximal k-edge-connected subgraphs in large networks by random contraction. In: CIKM, pp. 909–918 (2013)

    Google Scholar 

  2. Batagelj, V., Zaversnik, M.: An o(m) algorithm for cores decomposition of networks. arXiv preprint cs/0310049 (2003)

    Google Scholar 

  3. Berlowitz, D., Cohen, S., Kimelfeld, B.: Efficient enumeration of maximal k-plexes. In: SIGMOD, pp. 431–444 (2015)

    Google Scholar 

  4. Broder, A., Kumar, R., Maghoul, F., Raghavan, P., Rajagopalan, S., Stata, R., Tomkins, A., Wiener, J.: Graph structure in the web. Comput. Netw. 33(1), 309–320 (2000)

    Article  Google Scholar 

  5. Chang, L., Yu, J.X., Qin, L., Lin, X., Liu, C., Liang, W.: Efficiently computing k-edge connected components via graph decomposition. In: SIGMOD, pp. 205–216 (2013)

    Google Scholar 

  6. Cheng, J., Ke, Y., Chu, S., Özsu, M.T.: Efficient core decomposition in massive networks. In: ICDE, pp. 51–62 (2011)

    Google Scholar 

  7. Cui, W., Xiao, Y., Wang, H., Wang, W.: Local search of communities in large graphs. In: SIGMOD, pp. 991–1002 (2014)

    Google Scholar 

  8. Diestel, R.: Graph Theory. Graduate Texts in Mathematics. Springer, Heidelberg (2005)

    MATH  Google Scholar 

  9. Esfahanian, A.H., Louis Hakimi, S.: On computing the connectivities of graphs and digraphs. Networks 14(2), 355–366 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  10. Even, S., Tarjan, R.E.: Network flow and testing graph connectivity. SIAM J. Comput. 4(4), 507–518 (1975)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  12. Hariharan, R., Kavitha, T., Panigrahi, D., Bhalgat, A.: An o(mn) gomory-hu tree construction algorithm for unweighted graphs. In: ACM Symposium on Theory of Computing, pp. 605–614 (2007)

    Google Scholar 

  13. Huang, X., Cheng, H., Qin, L., Tian, W., Yu, J.X.: Querying k-truss community in large and dynamic graphs. In: SIGMOD, pp. 1311–1322 (2014)

    Google Scholar 

  14. Kargar, M., An, A.: Keyword search in graphs: finding r-cliques. PVLDB 4(10), 681–692 (2011)

    Google Scholar 

  15. Lee, C., Reid, F., McDaid, A., Hurley, N.: Detecting highly overlapping community structure by greedy clique expansion. arXiv preprint arXiv:1002.1827 (2010)

  16. Mokken, R.J.: Cliques, clubs and clans. Qual. Quant. 13(2), 161–173 (1979)

    Article  Google Scholar 

  17. Molloy, M., Reed, B.: The size of the giant component of a random graph with a given degree sequence. Comb. Probab. Comput. 7(3), 295–305 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  18. Palla, G., Derényi, I., Farkas, I., Vicsek, T.: Uncovering the overlapping community structure of complex networks in nature and society. Nature 435(7043), 814–818 (2005)

    Article  Google Scholar 

  19. Pattillo, J., Youssef, N., Butenko, S.: On clique relaxation models in network analysis. Eur. J. Oper. Res. 226(1), 9–18 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  20. Sozio, M., Gionis, A.: The community-search problem and how to plan a successful cocktail party. In: SIGKDD, pp. 939–948 (2010)

    Google Scholar 

  21. Stoer, M., Wagner, F.: A simple min-cut algorithm. J. ACM (JACM) 44(4), 585–591 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  22. Wang, J., Cheng, J.: Truss decomposition in massive networks. PVLDB 5(9), 812–823 (2012)

    Google Scholar 

  23. Wang, N., Zhang, J., Tan, K.L., Tung, A.K.: On triangulation-based dense neighborhood graph discovery. PVLDB 4(2), 58–68 (2010)

    Google Scholar 

  24. Wu, Y., Jin, R., Li, J., Zhang, X.: Robust local community detection: on free rider effect and its elimination. PVLDB 8(7), 798–809 (2015)

    Google Scholar 

  25. Wu, Y., Jin, R., Zhu, X., Zhang, X.: Finding dense and connected subgraphs in dual networks. In: ICDE, pp. 915–926 (2015)

    Google Scholar 

  26. Yang, J., Leskovec, J.: Defining and evaluating network communities based on ground-truth. In: ICDM, pp. 745–754 (2012)

    Google Scholar 

  27. Zeng, Z., Wang, J., Zhou, L., Karypis, G.: Coherent closed quasi-clique discovery from large dense graph databases. In: KDD, pp. 797–802 (2006)

    Google Scholar 

  28. Zhou, R., Liu, C., Yu, J.X., Liang, W., Chen, B., Li, J.: Finding maximal k-edge-connected subgraphs from a large graph. In: EDBT, pp. 480–491 (2012)

    Google Scholar 

Download references

Acknowledgments

This research is partially supported by the National NSFC (No. 61272182, 61100028, 61332014, U1401256, 61672144), the Fundamental Research Funds for the Central Universities (N150402002, N150404008), the National Research Foundation, Prime Ministers Office, Singapore under its International Research Centres in Singapore Funding Initiative and the Pinnacle lab for Analytics at SMU.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yuhai Zhao .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Li, Y., Zhao, Y., Wang, G., Zhu, F., Wu, Y., Shi, S. (2017). Effective k-Vertex Connected Component Detection in Large-Scale Networks. In: Candan, S., Chen, L., Pedersen, T., Chang, L., Hua, W. (eds) Database Systems for Advanced Applications. DASFAA 2017. Lecture Notes in Computer Science(), vol 10178. Springer, Cham. https://doi.org/10.1007/978-3-319-55699-4_25

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-55699-4_25

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-55698-7

  • Online ISBN: 978-3-319-55699-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics