Skip to main content
Springer Nature Link
Log in

Core maintenance for hypergraph streams

  • Published:
World Wide Web Aims and scope Submit manuscript

Abstract

This paper studies batch processing of core maintenance in hypergraph streams. We focus on updating the coreness of each vertex after the hypergraph evolves. Unlike existing works that mainly focus on exact coreness updates for the single hyperedge dynamic or approximate update, we propose the first known batch processing algorithms for exact core maintenance with insertions or deletions of multiple hyperedges. By proposing a hyperedge structure Joint Hyperedge Set, we tackle the challenges of quantifying the range of coreness change and finding potential vertices whose coreness may update. In addition, we accelerate coreness updates even further by finding structures that enable parallel execution. Extensive experiments illustrate the efficiency, scalability, and effectiveness of our batch core maintenance algorithms on real-world hypergraphs. It shows that our algorithms can be faster than the single hyperedge processing approaches by a factor of nearly half the number of hyperedges processed, and our parallel algorithms achieve linear acceleration with the increasing number of threads.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Algorithm 1
Fig. 1
Algorithm 2
Algorithm 3
Algorithm 4
Algorithm 5
Algorithm 6
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Availability of data and materials

All the datasets can be accessed from http://www.cs.cornell.edu/~arb/data/

Notes

  1. http://www.cs.cornell.edu/~arb/data/.

  2. All the datasets can be downloaded in ARB [46].

References

  1. Berge, C.: Graphs and hypergraphs. In: North-Holland (1973)

  2. Ouvrard, X.: Hypergraphs: an introduction and review. arXiv:2002.05014 (2020)

  3. Chodrow, P.S., Mellor, A.: Annotated hypergraphs: Models and applications. Appl. Netw. Sci. 5, 9 (2020)

    Article  Google Scholar 

  4. Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., Hwang, D.-U.: Complex networks: Structure and dynamics. Physics Reports 424, 175–308 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chang, L., Qin, L.: Cohesive subgraph computation over large sparse graphs. In: 35th IEEE International Conference on Data Engineering, pp. 2068–2071 (2019)

  6. Tsourakakis, C.E.: The k-clique densest subgraph problem. In: Proceedings of the 24th International Conference on World Wide Web, WWW, pp. 1122–1132 (2015)

  7. Li, Y., Liu, J., Zhao, H., Sun, J., Zhao, Y., Wang, G.: Efficient continual cohesive subgraph search in large temporal graphs. World Wide Web 24, 1483–1509 (2021)

    Article  Google Scholar 

  8. Zhou, W., Huang, H., Hua, Q.-S., Yu, D., Jin, H., Fu, X.: Core decomposition and maintenance in weighted graph. World Wide Web 24, 541–561 (2021)

    Article  Google Scholar 

  9. Zhou, Z., Zhang, W., Zhang, F., Chu, D., Li, B.: Vek: a vertex-oriented approach for edge k-core problem. World Wide Web 25(2), 723–740 (2022)

    Article  Google Scholar 

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

  11. Sun, R., Chen, C., Wang, X., Wu, Y., Zhang, M., Liu, X.: The art of characterization in large networks: Finding the critical attributes. World Wide Web 25(2), 655–677 (2022)

    Article  Google Scholar 

  12. Sun, R., Chen, C., Liu, X., Xu, S., Wang, X., Lin, X.: Critical nodes identification in large networks: the inclined and detached models. World Wide Web 25(3), 1315–1341 (2022)

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  15. Leng, M., Sun, L., Bian, J., Ma, Y.: An o(m) algorithm for cores decomposition of undirected hypergraph. J Chinese Comput Syst 34(11), 2568–2573 (2013)

    Google Scholar 

  16. Malliaros, F.D., Giatsidis, C., Papadopoulos, A.N., Vazirgiannis, M.: The core decomposition of networks: theory, algorithms and applications. VLDB J. 29(1), 61–92 (2020). https://doi.org/10.1007/s00778-019-00587-4

    Article  Google Scholar 

  17. Hébert-Dufresne, L., Allard, A., Young, J.-G., Dubé, L.J.: Percolation on random networks with arbitrary k-core structure. Phys. Rev. E 88(6), 062820 (2013). https://doi.org/10.1103/PhysRevE.88.062820

    Article  Google Scholar 

  18. Shin, K., Eliassi-Rad, T., Faloutsos, C.: Corescope: Graph mining using k-core analysis - patterns, anomalies and algorithms. In: IEEE 16th International Conference on Data Mining, ICDM, pp. 469–478 (2016). https://doi.org/10.1109/ICDM.2016.0058

  19. Shin, K., Eliassi-Rad, T., Faloutsos, C.: Patterns and anomalies in k-cores of real-world graphs with applications. Knowl. Inf. Syst. 54(3), 677–710 (2018)

    Article  Google Scholar 

  20. Lahav, N., Ksherim, B., Ben-Simon, E., Maron-Katz, A., Cohen, R., Havlin, S.: K-shell decomposition reveals hierarchical cortical organization of the human brain. New J. Phys. 18(8), 083013 (2016). https://doi.org/10.1088/1367-2630/18/8/083013

    Article  Google Scholar 

  21. Alistarh, D., Iglesias, J., Vojnovic, M.: Streaming min-max hypergraph partitioning. In: Annual Conference on Neural Information Processing Systems, pp. 1900–1908 (2015)

  22. McGregor, A.: Graph stream algorithms: a survey. SIGMOD Rec. 43(1), 9–20 (2014)

    Article  Google Scholar 

  23. Dhulipala, L., Blelloch, G.E., Shun, J.: Low-latency graph streaming using compressed purely-functional trees. In: Proceedings of the ACM SIGPLAN Conference on Programming Language Design and Implementation,, pp. 918–934 (2019)

  24. Li, R.-H., Su, J., Qin, L., Yu, J.X., Dai, Q.: Persistent community search in temporal networks. In: 2018 IEEE 34th International Conference on Data Engineering (ICDE), pp. 797–808 (2018)

  25. Zhang, F., Gou, X., Zou, L.: Top-k heavy weight triangles listing on graph stream. World Wide Web, 1–25 (2022)

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

    Article  Google Scholar 

  27. Li, R., Yu, J.X., Mao, R.: Efficient core maintenance in large dynamic graphs. IEEE Trans. Knowl. Data Eng. 26(10), 2453–2465 (2014)

    Article  Google Scholar 

  28. Sariyüce, A.E., Gedik, B., Jacques-Silva, G., Wu, K., Çatalyürek, Ü.V.: Incremental k-core decomposition: algorithms and evaluation. VLDB J. 25(3), 425–447 (2016)

    Article  Google Scholar 

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

  30. Luo, Q., Yu, D., Li, F., Dou, Z., Cai, Z., Yu, J., Cheng, X.: Distributed core decomposition in probabilistic graphs. In: 8th International Conference Computational Data and Social Networks Proceedings. Lecture Notes in Computer Science, 11917, pp. 16–32. Springer, Ho Chi Minh City, Vietnam (2019)

  31. 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 Distributed Syst. 31(6), 1287–1300 (2020)

    Article  Google Scholar 

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

    Article  Google Scholar 

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

  34. Sun, B., Chan, T.-H., Sozio, M.: Fully dynamic approximate k-core decomposition in hypergraphs. ACM Trans. Knowl. Discov. Data 14(4), 39–13921 (2020)

    Article  Google Scholar 

  35. Luo, Q., Yu, D., Cai, Z., Lin, X., Cheng, X.: Hypercore maintenance in dynamic hypergraphs. In: IEEE International Conference on Data Engineering, pp. 2051–2056 (2021)

  36. Gabert, K., Pinar, A., Çatalyürek, Ü.V.: Shared-memory scalable k-core maintenance on dynamic graphs and hypergraphs. In: IEEE International Parallel and Distributed Processing Symposium Workshops, pp. 998–1007 (2021)

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

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

  39. Leng, M., Sun, L.: Comparative experiment of the core property of weighted hyper-graph based on the ispd98 benchmark. J. Inf. Computationalence 10(8), 2279–2290 (2013)

    Google Scholar 

  40. Jiang, J., Mitzenmacher, M., Thaler, J.: Parallel peeling algorithms. ACM Trans. Parallel Comput. 3(1), 7–1727 (2016)

    Article  Google Scholar 

  41. Shun, J.: Practical parallel hypergraph algorithms. In: PPoPP ’20: 25th ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming, pp. 232–249 (2020)

  42. Montresor, A., Pellegrini, F.D., Miorandi, D.: Distributed k-core decomposition. In: Proceedings of the 30th Annual ACM Symposium on Principles of Distributed Computing, PODC, pp. 207–208 (2011)

  43. Lü, L., Zhou, T., Zhang, Q.-M., Stanley, H.E.: The h-index of a network node and its relation to degree and coreness. Nature Commun. 7(1), 10168–10168 (2016)

    Article  Google Scholar 

  44. Sariyüce, A.E., Seshadhri, C., Pinar, A.: Local algorithms for hierarchical dense subgraph discovery. Proc. VLDB Endow. 12(1), 43–56 (2018)

    Article  Google Scholar 

  45. Gabert, K., Pinar, A., Çatalyrek, U.V.: A unifying framework to identify dense subgraphs on streams: Graph nuclei to hypergraph cores. In: International Conference on Web Search and Data Mining, pp. 689–697 (2021)

  46. Benson, A.R., Abebe, R., Schaub, M.T., Jadbabaie, A., Kleinberg, J.M.: Simplicial closure and higher-order link prediction. Proc. Natl. Acad. Sci. USA 115(48), 11221–11230 (2018)

    Article  Google Scholar 

Download references

Funding

National Key Research and Development Program of China under Grant 2020YFB1005900, National Natural Science Foundation of China (NSFC) under Grant 62122042, Shandong University multidisciplinary research and innovation team of young scholars under Grant 2020QNQT017

Author information

Authors and Affiliations

  1. School of Computer Science and Technology, Shandong University, 72 Binhai, Qingdao, Shandong, 266200, People’s Republic of China

    Qi Luo, Dongxiao Yu, Yanwei Zheng & Xiuzhen Cheng

  2. Department of Computer Science, Georgia State University, 25 Park Place, Atlanta, Georgia, GA 30303, USA

    Zhipeng Cai

  3. Antai College of Economics and Management, Shanghai Jiao Tong University, 535 Fahuazhen, Shanghai, 200052, People’s Republic of China

    Xuemin Lin

Authors
  1. Qi Luo
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Dongxiao Yu
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Zhipeng Cai
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Yanwei Zheng
    View author publications

    You can also search for this author inPubMed Google Scholar

  5. Xiuzhen Cheng
    View author publications

    You can also search for this author inPubMed Google Scholar

  6. Xuemin Lin
    View author publications

    You can also search for this author inPubMed Google Scholar

Contributions

Qi Luo and Dongxiao Yu wrote the manuscript, Yanwei Zheng collected the data, and Xiuzhen Cheng and Xuemin Lin analyzed the results. All authors reviewed the results and approved the final version of the manuscript

Corresponding author

Correspondence to Dongxiao Yu.

Ethics declarations

Competing Interests

We declare that the authors have no known competing interests or personal relationships that might be perceived to influence the discussion reported in this paper

Ethical Approval

not applicable

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Luo, Q., Yu, D., Cai, Z. et al. Core maintenance for hypergraph streams. World Wide Web 26, 3709–3733 (2023). https://doi.org/10.1007/s11280-023-01196-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11280-023-01196-6

Keywords