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Core Decomposition, Maintenance and Applications

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Complexity and Approximation

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12000))

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Abstract

Structures of large graphs have attracted much attention in recent years, including k-clique, k-core, k-truss, k-club, to name just a few. These structures can help detect the most cohesive or most influential subgraphs of social networks and other massive graphs. In this survey, we summarize the research on k-core, which is the maximal connected subgraph of a graph and the degree for each vertex is equal to or greater than k. We will address the core decomposition problem, the core maintenance problem, and a few applications of k-core.

This research was supported in part by the National Natural Science Foundation of China (11971447, 11871442), the Natural Science Foundation of Shandong Province of China (ZR2017QA010), and the Fundamental Research Funds for the Central Universities (201964006).

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References

  1. Seidman, S.B.: Network structure and minimum degree. Soc. Netw. 5(3), 269–287 (1983)

    Article  MathSciNet  Google Scholar 

  2. Batagelj, V., Zaversnik, M.: An O(m) algorithm for cores decomposition of networks. In: The Computing Research Repository (CoRR). arXiv:cs.DS/0310049 (2003)

  3. Batagelj, V., Zaveršnik, M.: Fast algorithms for determining (generalized) core groups in social networks. Adv. Data Anal. Classif. 5(2), 129–145 (2011)

    Article  MathSciNet  Google Scholar 

  4. Cheng, J., Ke, Y., Chu, S., Özsu, M.T.: Efficient core decomposition in massive networks. In: 27th International Conference on Data Engineering (ICDE), pp. 51–62. IEEE, Hannover (2011)

    Google Scholar 

  5. Garas, A., Schweitzer, F., Havlin, S.: A k-shell decomposition method for weighted networks. New J. Phys. 14(8), 083030 (2012)

    Article  Google Scholar 

  6. Montresor, A., De Pellegrini, F., Miorandi, D.: Distributed k-core decomposition. Trans. Parallel Distrib. Syst. 24(2), 288–300 (2012)

    Article  Google Scholar 

  7. Jakma, P., Orczyk, M., Perkins, C.S., Fayed, M.: Distributed k-core decomposition of dynamic graphs. In: Proceedings of the 2012 ACM Conference on CoNEXT Student Workshop, pp. 39–40. ACM, Nice (2012)

    Google Scholar 

  8. Khaouid, W., Barsky, M., Srinivasan, V., Thomo, A.: K-core decomposition of large networks on a single PC. Proc. VLDB Endow. 9(1), 13–23 (2015)

    Article  Google Scholar 

  9. Govindan, P., Wang, C., Xu, C., Duan, H., Soundarajan, S.: The k-peak decomposition: mapping the global structure of graphs. In: Proceedings of the 26th International Conference on World Wide Web, pp. 1441–1450. International World Wide Web Conferences Steering Committee, Perth (2017)

    Google Scholar 

  10. Mandal, A., Al Hasan, M.: A distributed k-core decomposition algorithm on spark. In: 2017 IEEE International Conference on Big Data (Big Data), pp. 976–981. IEEE, Boston (2017)

    Google Scholar 

  11. Bonchi, F., Gullo, F., Kaltenbrunner, A., Volkovich, Y.: Core decomposition of uncertain graphs. In: Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1316–1325. ACM, New York (2014)

    Google Scholar 

  12. Peng, Y., Zhang, Y., Zhang, W., Lin, X., Qin, L.: Efficient probabilistic k-core computation on uncertain graphs. In: 2018 IEEE 34th International Conference on Data Engineering (ICDE), pp. 1192–1203. IEEE, Paris (2018)

    Google Scholar 

  13. Tripathy, A., Hohman, F., Chau, D.H., Green, O.: Scalable K-core decomposition for static graphs using a dynamic graph data structure. In: 2018 IEEE International Conference on Big Data (Big Data), pp. 1134–1141. IEEE, Seattle (2018)

    Google Scholar 

  14. Wen, D., Qin, L., Zhang, Y., Lin, X., Yu, J.X.: I/o efficient core graph decomposition at web scale. In: 2016 IEEE 32nd International Conference on Data Engineering (ICDE), pp. 133–144. IEEE, Helsinki (2016)

    Google Scholar 

  15. Wen, D., Qin, L., Zhang, Y., Lin, X., Yu, J.X.: I/O efficient core graph decomposition: application to degeneracy ordering. IEEE Trans. Knowl. Data Eng. 31(1), 75–90 (2018)

    Article  Google Scholar 

  16. Sarıyüce, A.E., Gedik, B., Jacques-Silva, G., Wu, K.L., Çatalyürek, Ü.V.: Streaming algorithms for k-core decomposition. Proc. VLDB Endow. 6(6), 433–444 (2013)

    Article  Google Scholar 

  17. Sarıyüce, A.E., Gedik, B., Jacques-Silva, G., Wu, K.L., Çatalyürek, Ü.V.: Incremental k-core decomposition: algorithms and evaluation. VLDB J. Int. J. Very Large Data Bases 25(3), 425–447 (2016)

    Article  Google Scholar 

  18. Li, R.H., Yu, J.X., Mao, R.: Efficient core maintenance in large dynamic graphs. IEEE Trans. Knowl. Data Eng. 26(10), 2453–2465 (2013)

    Article  Google Scholar 

  19. Aksu, H., Canim, M., Chang, Y.C., Korpeoglu, I., Ulusoy, Ö.: Distributed k-core view materialization and maintenance for large dynamic graphs. IEEE Trans. Knowl. Data Eng. 26(10), 2439–2452 (2014)

    Article  Google Scholar 

  20. Aridhi, S., Brugnara, M., Montresor, A., Velegrakis, Y.: Distributed k-core decomposition and maintenance in large dynamic graphs. In: Proceedings of the 10th ACM International Conference on Distributed and Event-based Systems, pp. 161–168. ACM, Irvine (2016)

    Google Scholar 

  21. Zhang, Y., Yu, J.X., Zhang, Y., Qin, L.: A fast order-based approach for core maintenance. In: 2017 IEEE 33rd International Conference on Data Engineering (ICDE), pp. 337–348. IEEE, San Diego (2017)

    Google Scholar 

  22. Wang, N., Yu, D., Jin, H., Qian, C., Xie, X., Hua, Q.S.: Parallel algorithm for core maintenance in dynamic graphs. In: 2017 IEEE 37th International Conference on Distributed Computing Systems (ICDCS), pp. 2366–2371. IEEE, Atlanta (2017)

    Google Scholar 

  23. Jin, H., Wang, N., Yu, D., Hua, Q.S., Shi, X., Xie, X.: Core maintenance in dynamic graphs: a parallel approach based on matching. IEEE Trans. Parallel Distrib. Syst. 29(11), 2416–2428 (2018)

    Article  Google Scholar 

  24. Bonchi, F., Gullo, F., Kaltenbrunner, A.: Core Decomposition of Massive, Information-Rich Graphs. In: Alhajj, R., Rokne, J. (eds.) Encyclopedia of Social Network Analysis and Mining. Springer, New York (2018). https://doi.org/10.1007/978-1-4939-7131-2_110176

    Chapter  Google Scholar 

  25. Yue, L., Wen, D., Cui, L., Qin, L., Zheng, Y.: K-connected cores computation in large dual networks. In: Pei, J., Manolopoulos, Y., Sadiq, S., Li, J. (eds.) DASFAA 2018. LNCS, vol. 10827, pp. 169–186. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-91452-7_12

    Chapter  Google Scholar 

  26. Wang, K., Cao, X., Lin, X., Zhang, W., Qin, L.: Efficient computing of radius-bounded k-cores. In: 2018 IEEE 34th International Conference on Data Engineering (ICDE), pp. 233–244. IEEE, Paris (2018)

    Google Scholar 

  27. Zhang, F., Zhang, Y., Qin, L., Zhang, W., Lin, X.: When engagement meets similarity: efficient (k, r)-core computation on social networks. Proc. VLDB Endow. 10(10), 998–1009 (2017)

    Article  Google Scholar 

  28. Laishram, R., Sariyüce, A.E., Eliassi-Rad, T., Pinar, A., Soundarajan, S.: Measuring and improving the core resilience of networks. In: Proceedings of the 2018 World Wide Web Conference, pp. 609–618. International World Wide Web Conferences Steering Committee, Lyon (2018)

    Google Scholar 

  29. Li, R.H., Qin, L., Yu, J.X., Mao, R.: Finding influential communities in massive networks. VLDB J. Int. J. Very Large Data Bases 26(6), 751–776 (2017)

    Article  Google Scholar 

  30. Bae, J., Kim, S.: Identifying and ranking influential spreaders in complex networks by neighborhood coreness. Phys. A Stat. Mech. Appl. 395, 549–559 (2014)

    Article  MathSciNet  Google Scholar 

  31. Rossi, M.E.G., Malliaros, F.D., Vazirgiannis, M.: Spread it good, spread it fast: identification of influential nodes in social networks. In: Proceedings of the 24th International Conference on World Wide Web, pp. 101–102. ACM, Florence (2015)

    Google Scholar 

  32. Alduaiji, N., Datta, A.: An empirical study on sentiments in twitter communities. In: 2018 IEEE International Conference on Data Mining Workshops (ICDMW), pp. 1166–1172. IEEE, Singapore (2018)

    Google Scholar 

  33. Barbieri, N., Bonchi, F., Galimberti, E., Gullo, F.: Efficient and effective community search. Data Min. Knowl. Disc. 29(5), 1406–1433 (2015)

    Article  MathSciNet  Google Scholar 

  34. Papadopoulos, S., Kompatsiaris, Y., Vakali, A., Spyridonos, P.: Community detection in social media. Data Min. Knowl. Disc. 24(3), 515–554 (2012)

    Article  Google Scholar 

  35. Nasir, M.A.U., Gionis, A., Morales, G.D.F., Girdzijauskas, S.: Fully dynamic algorithm for top-k densest subgraphs. In: Proceedings of the 2017 ACM on Conference on Information and Knowledge Management, pp. 1817–1826. ACM, Singapore (2017)

    Google Scholar 

  36. Qu, Y., et al.: Using K-core decomposition on class dependency networks to improve bug prediction model’s practical performance. IEEE Trans. Softw. Eng. 1 (2019). https://doi.org/10.1109/TSE.2019.2892959

  37. Cheng, Y., Lu, C., Wang, N.: Local k-core clustering for gene networks. In: 2013 IEEE International Conference on Bioinformatics and Biomedicine, pp. 9–15. IEEE, Shanghai (2013)

    Google Scholar 

  38. Ma, J., Balasundaram, B.: On the chance-constrained minimum spanning k-core problem. J. Global Optim. 74(4), 783–801 (2019)

    Article  MathSciNet  Google Scholar 

  39. Alvarez-Hamelin, J.I., Dall’Asta, L., Barrat, A., Vespignani, A.: Large scale networks fingerprinting and visualization using the k-core decomposition. In: Advances in Neural Information Processing Systems, pp. 41–50 (2006)

    Google Scholar 

  40. Eppstein, D., Löffler, M., Strash, D.: Listing all maximal cliques in sparse graphs in near-optimal time. In: Cheong, O., Chwa, K.-Y., Park, K. (eds.) ISAAC 2010. LNCS, vol. 6506, pp. 403–414. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17517-6_36

    Chapter  Google Scholar 

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Authors and Affiliations

  1. School of Mathematical Sciences, Ocean University of China, Qingdao, 266100, Shandong, People’s Republic of China

    Feiteng Zhang, Bin Liu & Qizhi Fang

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  1. Feiteng Zhang
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  2. Bin Liu
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  3. Qizhi Fang
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Correspondence to Bin Liu .

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Editors and Affiliations

  1. The University of Texas at Dallas, Richardson, TX, USA

    Ding-Zhu Du

  2. University of Massachusetts Lowell, Lowell, MA, USA

    Jie Wang

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Zhang, F., Liu, B., Fang, Q. (2020). Core Decomposition, Maintenance and Applications. In: Du, DZ., Wang, J. (eds) Complexity and Approximation. Lecture Notes in Computer Science(), vol 12000. Springer, Cham. https://doi.org/10.1007/978-3-030-41672-0_12

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  • DOI: https://doi.org/10.1007/978-3-030-41672-0_12

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