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Minimum Degree-Based Core Decomposition

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Cohesive Subgraph Computation over Large Sparse Graphs

Part of the book series: Springer Series in the Data Sciences ((SSDS))

Abstract

In this chapter, we discuss efficient techniques for computing the minimum degree-based graph decomposition (aka, core decomposition). Preliminaries are given in Section 3.1. A linear-time algorithm is presented in Section 3.2, while h-index-based local algorithms that can be naturally made parallel are presented in Section 3.3.

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Notes

  1. 1.

    https://github.com/LijunChang/Cohesive_subgraph_book/blob/master/data_structures/UnionFind.h.

References

  1. Vladimir Batagelj and Matjaz Zaversnik. An o(m) algorithm for cores decomposition of networks. CoRR, cs.DS/0310049, 2003.

    Google Scholar 

  2. Francesco Bonchi, Francesco Gullo, Andreas Kaltenbrunner, and Yana Volkovich. Core decomposition of uncertain graphs. In Proc. of KDD’14, pages 1316–1325, 2014.

    Google Scholar 

  3. Lijun Chang, Xuemin Lin, Lu Qin, Jeffrey Xu Yu, and Wenjie Zhang. Index-based optimal algorithms for computing Steiner components with maximum connectivity. In Proc. of SIGMOD’15, 2015.

    Google Scholar 

  4. James Cheng, Yiping Ke, Shumo Chu, and M. Tamer Özsu. Efficient core decomposition in massive networks. In Proc. of ICDE’11, pages 51–62, 2011.

    Google Scholar 

  5. Norishige Chiba and Takao Nishizeki. Arboricity and subgraph listing algorithms. SIAM J. Comput., 14(1):210–223, 1985.

    Article  MathSciNet  Google Scholar 

  6. Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. Introduction to Algorithms (3. ed.). MIT Press, 2009.

    Google Scholar 

  7. A. Erdem Sariyuce, C. Seshadhri, and A. Pinar. Parallel Local Algorithms for Core, Truss, and Nucleus Decompositions. ArXiv e-prints, 2017.

    Google Scholar 

  8. Christos Giatsidis, Dimitrios M. Thilikos, and Michalis Vazirgiannis. Evaluating cooperation in communities with the k-core structure. In Proc. of ASONAM’11, pages 87–93, 2011.

    Google Scholar 

  9. Christos Giatsidis, Dimitrios M. Thilikos, and Michalis Vazirgiannis. D-cores: measuring collaboration of directed graphs based on degeneracy. Knowl. Inf. Syst., 35(2):311–343, 2013.

    Article  Google Scholar 

  10. J. E. Hirsch. An index to quantify an individual’s scientific research output. Proceedings of the National Academy of Sciences of the United States of America, 102(46):16569–16572, 2005.

    Article  Google Scholar 

  11. Wissam Khaouid, Marina Barsky, Venkatesh Srinivasan, and Alex Thomo. K-core decomposition of large networks on a single pc. PVLDB, 9(1):13–23, 2015.

    Google Scholar 

  12. Rong-Hua Li, Lu Qin, Jeffrey Xu Yu, and Rui Mao. Influential community search in large networks. PVLDB, 8(5):509–520, 2015.

    Article  Google Scholar 

  13. Rong-Hua Li, Jeffrey Xu Yu, and Rui Mao. Efficient core maintenance in large dynamic graphs. IEEE Trans. Knowl. Data Eng., 26(10):2453–2465, 2014.

    Article  Google Scholar 

  14. Don R. Lick and Arthur T. White. k-degenerate graphs. Canadian Journal of Mathematics, 22:1082–1096, 1970.

    Article  Google Scholar 

  15. Linyuan Lü, Tao Zhou, Qian-Ming Zhang, and H. E. Stanley. The h-index of a network node and its relation to degree and coreness. Nature Communications, 7:10168, 2016.

    Google Scholar 

  16. Fragkiskos D. Malliaros, Apostolos N. Papadopoulos, and Michalis Vazirgiannis. Core decomposition in graphs: Concepts, algorithms and applications. In Proc. of EDBT’16, pages 720–721, 2016.

    Google Scholar 

  17. David W. Matula and Leland L. Beck. Smallest-last ordering and clustering and graph coloring algorithms. J. ACM, 30(3):417–427, 1983.

    Article  MathSciNet  Google Scholar 

  18. Alberto Montresor, Francesco De Pellegrini, and Daniele Miorandi. Distributed k-core decomposition. In Proc. of PODC’11, pages 207–208, 2011.

    Google Scholar 

  19. Francesco De Pellegrini, Alberto Montresor, and Daniele Miorandi. Distributed k-core decomposition. IEEE Transactions on Parallel & Distributed Systems, 24:288–300, 2013.

    Article  Google Scholar 

  20. Ahmet Erdem Sariyüce, Bugra Gedik, Gabriela Jacques-Silva, Kun-Lung Wu, and Ümit V. Çatalyürek. Streaming algorithms for k-core decomposition. PVLDB, 6(6):433–444, 2013.

    Article  Google Scholar 

  21. Ahmet Erdem Sariyüce, Bugra Gedik, Gabriela Jacques-Silva, Kun-Lung Wu, and Ümit V. Çatalyürek. Incremental k-core decomposition: algorithms and evaluation. VLDB J., 25(3):425–447, 2016.

    Google Scholar 

  22. Ahmet Erdem Sariyüce and Ali Pinar. Fast hierarchy construction for dense subgraphs. PVLDB, 10(3):97–108, 2016.

    Google Scholar 

  23. Stephen B. Seidman. Network structure and minimum degree. Social Networks, 5(3):269–287, 1983.

    Article  MathSciNet  Google Scholar 

  24. Dong Wen, Lu Qin, Ying Zhang, Xuemin Lin, and Jeffrey Xu Yu. I/O efficient core graph decomposition at web scale. In Proc. of ICDE’16, 2016.

    Google Scholar 

  25. Yikai Zhang, Jeffrey Xu Yu, Ying Zhang, and Lu Qin. A fast order-based approach for core maintenance. In Proc. of ICDE’11, pages 337–348, 2017.

    Google Scholar 

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Chang, L., Qin, L. (2018). Minimum Degree-Based Core Decomposition. In: Cohesive Subgraph Computation over Large Sparse Graphs. Springer Series in the Data Sciences. Springer, Cham. https://doi.org/10.1007/978-3-030-03599-0_3

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