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Core decomposition and maintenance in weighted graph

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Abstract

Coreness is an important index to reflect the cohesiveness of a graph. The problems of core computation in static graphs and core update in dynamic graphs, known as the core decomposition and core maintenance problems respectively, have been extensively studied in previous work. However, most of these work focus on unweighted graphs. Considering that graphs are weighted in a lot of realistic applications, it is indispensable to extend the coreness to weighted graphs and devise efficient algorithms for weighted core decomposition and weighted core maintenance. In this work, we present a new definition of weighted coreness for vertices in a weighted graph, by taking into account the weights of vertices, which makes the coreness in unweighted graph be a special case. We propose efficient algorithms for both weighted core decomposition and weighted core maintenance problems. The coreness of vertices can be computed in linear time by the proposed decomposition algorithm, while the proposed core maintenance algorithm can process multiple-edge insertions/deletions simultaneously, which greatly reduces the core update time. Comprehensive experiments on both realistic networks and temporal graphs exhibit our algorithms are efficient and scalable.

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References

  1. Al-Garadi, M.A., Varathan, K.D., Ravana, S.D.: Identification of influential spreaders in online social networks using interaction weighted k-core decomposition method. Physica A Statistical Mechanics and Its Applications, S0378437116308068 (2016)

  2. 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)

  3. 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 (2016)

  4. Batagelj, V., Mrvar, A., Zaveršnik, M.: Partitioning approach to visualization of large graphs. In: International Symposium on Graph Drawing, pp. 90–97. Springer (1999)

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

  6. Cheng, J., Ke, Y., Chu, S., Özsu, M. T.: Efficient core decomposition in massive networks. In: Abiteboul, S., Böhm, K., Koch, C., Tan, K. (eds.) Proceedings of the 27th International Conference on Data Engineering, ICDE, pp. 51–62. IEEE Computer Society (2011)

  7. Cohen, J.: Trusses: Cohesive subgraphs for social network analysis. National Security Agency Technical Report 16, 3–1 (2008)

    Google Scholar 

  8. Dasari, N.S., Desh, R., Zubair, M.: Park: An efficient algorithm for k-core decomposition on multicore processors. In: 2014 IEEE International Conference on Big Data (Big Data), pp. 9–16. IEEE (2014)

  9. Eidsaa, M., Almaas, E.: S-core network decomposition: A generalization of k-core analysis to weighted networks. Phys. Rev. E 88(6), 062,819 (2013)

    Article  Google Scholar 

  10. Fortunato, S.: Community detection in graphs. Phys. Rep. 486 (3–5), 75–174 (2010)

    Article  MathSciNet  Google Scholar 

  11. Garas, A., Schweitzer, F., Havlin, S.: A k-shell decomposition method for weighted networks. J. Phys. 14(8), 083,030 (2012)

    MATH  Google Scholar 

  12. Hua, Q., Shi, Y., Yu, D., Jin, H., Yu, J., Cai, Z., Cheng, X., Chen, H.: Faster parallel core maintenance algorithms in dynamic graphs. IEEE Trans. Parallel Distrib. Syst. 31(6), 1287–1300 (2020)

    Article  Google Scholar 

  13. Huang, C., Fu, Y., Sun, C.: Identify influential social network spreaders. In: 2014 IEEE International Conference on Data Mining Workshops, ICDM workshop, pp. 562–568. IEEE Computer Society (2014)

  14. 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 

  15. Khaouid, W., Barsky, M., Srinivasan, V., Thomo, A.: K-core decomposition of large networks on a single pc. Proceed. Vldb Endow. 9(1), 13–23 (2015)

    Article  Google Scholar 

  16. Kitsak, M., Gallos, L.K., Havlin, S., Liljeros, F., Muchnik, L., Stanley, H.E., Makse, H.A.: Identification of influential spreaders in complex networks. Nat. Phys. 6(11), 888–893 (2010)

    Article  Google Scholar 

  17. Leskovec, J., Krevl, A.: Snap datasets: Stanford large network dataset collection. http://snap.stanford.edu/data, p. 49 (2016) (2014)

  18. Li, R., Qin, L., Yu, J.X., Mao, R.: Influential community search in large networks. Proc. VLDB Endow. 8(5), 509–520 (2015)

    Article  Google Scholar 

  19. 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 

  20. Liu, B., Zhang, F.: Incremental algorithms of the core maintenance problem on edge-weighted graphs. IEEE Access 8, 63,872–63,884 (2020)

    Article  Google Scholar 

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

    Article  Google Scholar 

  22. Samudrala, R., Moult, J.: A graph-theoretic algorithm for comparative modeling of protein structure. J. Molec. Biol. 279(1), 287–302 (1998)

    Article  Google Scholar 

  23. 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 

  24. 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 (2017)

  25. Wei, B., Liu, J., Wei, D., Gao, C., Deng, Y.: Weighted k-shell decomposition for complex networks based on potential edge weights. Physica A: Statist. Mech. Appl. 420, 277–283 (2015)

    Article  Google Scholar 

  26. Wu, X., Wei, W., Tang, L., Lu, J., Lü, J.: Coreness and h-index for weighted networks. IEEE Transactions on Circuits and Systems I: Regular Papers (2019)

  27. Zhang, H., Zhao, H., Cai, W., Liu, J., Zhou, W.: Using the k-core decomposition to analyze the static structure of large-scale software systems. J. Supercomput. 53(2), 352–369 (2010)

    Article  Google Scholar 

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

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Acknowledgements

The work is supported by National Natural Science Foundation of China (No. 61802140, 61972447).

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Authors and Affiliations

  1. Services Computing Technology and System Lab / Big Data Technology and System Lab, Huazhong University of Science and Technology, Wuhan, China

    Wei Zhou, Hong Huang, Qiang-Sheng Hua & Hai Jin

  2. School of Computer Science and Technology, Shandong University, Qingdao, China

    Dongxiao Yu

  3. Institute of Computer Science, University of Goettingen, Goettingen, Germany

    Xiaoming Fu

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  1. Wei Zhou
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  2. Hong Huang
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  3. Qiang-Sheng Hua
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  4. Dongxiao Yu
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Correspondence to Hong Huang.

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Zhou, W., Huang, H., Hua, QS. et al. Core decomposition and maintenance in weighted graph. World Wide Web 24, 541–561 (2021). https://doi.org/10.1007/s11280-020-00857-0

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