Skip to main content
SpringerLink
Log in

Toward maintenance of hypercores in large-scale dynamic hypergraphs

  • Regular Paper
  • Published:
The VLDB Journal Aims and scope Submit manuscript

Abstract

In this paper, we study hypercore maintenance in large-scale dynamic hypergraphs. A hypergraph, whose hyperedges may contain a set of vertices rather than two vertices in pairwise graphs, can represent complex interactions in more sophisticated applications. However, the exponential number of hyperedges incurs unaffordable costs to recompute the hypercore number of vertices and hyperedges when updating a hypergraph. This motivates us to propose an efficient approach for exact hypercore maintenance with the intention of significantly reducing the hypercore updating time comparing with recomputation approaches. The proposed algorithms can pinpoint the vertices and hyperedges whose hypercore numbers have to be updated by only traversing a small sub-hypergraph. We also propose an index called Core-Index that can facilitate our maintenance algorithms. Extensive experiments on real-world and temporal hypergraphs demonstrate the superiority of our algorithms in terms of efficiency.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Notes

  1. https://www.cs.cornell.edu/arb/data/.

  2. https://skubuntu.com.

  3. https://dblp.uni-trier.de/.

  4. https://stackoverflow.com.

References

  1. Abello, J., Resende, M.G.C., Sudarsky, S.: Massive quasi-clique detection. In: 5th Latin American Symposium of Theoretical Informatics Proceedings. LATIN, Lecture Notes in Computer Science, vol. 2286, pp. 598–612. Springer, Cancun, Mexico (2002)

    Google Scholar 

  2. Alvarez-Hamelin, J.I., Dall’Asta, L., Barrat, A., Vespignani, A.: Large scale networks fingerprinting and visualization using the k-core decomposition. In: Neural Information Processing Systems, pp. 41–50. (2005)

  3. Alvarez-Hamelin, J.I., Dall’Asta, L., Barrat, A., Vespignani, A.: K-core decomposition of internet graphs: hierarchies, self-similarity and measurement biases. Netw. Heterog. Media 3(2), 371–393 (2008). https://doi.org/10.3934/nhm.2008.3.371

    Article  MathSciNet  MATH  Google Scholar 

  4. Arya, D., Worring, M.: Exploiting relational information in social networks using geometric deep learning on hypergraphs. In: Proceedings of the International Conference on Multimedia Retrieval, ICMR, pp. 117–125. ACM (2018)

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

  6. 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), E11221–E11230 (2018)

    Article  Google Scholar 

  7. Bu, J., Tan, S., Chen, C., Wang, C., Wu, H., Zhang, L., He, X.: Music recommendation by unified hypergraph: combining social media information and music content. In: Proceedings of the 18th International Conference on Multimedia, pp. 391–400. ACM (2010)

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

  9. Chang, L., Yu, J.X., Qin, L., Lin, X., Liu, C., Liang, W.: Efficiently computing k-edge connected components via graph decomposition. In: Proceedings of the ACM SIGMOD International Conference on Management of Data, pp. 205–216. ACM (2013). https://doi.org/10.1145/2463676.2465323

  10. Chen, J., Saad, Y.: Dense subgraph extraction with application to community detection. IEEE Trans. Knowl. Data Eng. 24(7), 1216–1230 (2012)

    Article  Google Scholar 

  11. Chen, L., Liu, C., Liao, K., Li, J., Zhou, R.: Contextual community search over large social networks. In: 35th IEEE International Conference on Data Engineering, pp. 88–99. IEEE (2019). https://doi.org/10.1109/ICDE.2019.00017

  12. Chen, L., Liu, C., Zhou, R., Li, J., Yang, X., Wang, B.: Maximum co-located community search in large scale social networks. Proc. VLDB Endow. 11(10), 1233–1246 (2018). https://doi.org/10.14778/3231751.3231755

    Article  Google Scholar 

  13. 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)

  14. Chlamtáč, E., Dinitz, M., Konrad, C., Kortsarz, G., Rabanca, G.: The densest k-subhypergraph problem. SIAM J. Discrete Math. 32(2), 1458–1477 (2018)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  16. Cohen, J.: Trusses: cohesive subgraphs for social network analysis. Natl. Secur. Agency Techn. Rep. 16, 3–29 (2008)

    Google Scholar 

  17. Daianu, M., Jahanshad, N., Nir, T.M., Toga, A.W., Jack, C.R.J., Weiner, M.W., Thompson, P.M.: Breakdown of brain connectivity between normal aging and alzheimer’s disease: a structural k-core network analysis. Brain Connect 3(4), 407–422 (2013). https://doi.org/10.1089/brain.2012.0137

    Article  Google Scholar 

  18. Das, A., Svendsen, M., Tirthapura, S.: Incremental maintenance of maximal cliques in a dynamic graph. VLDB J. 28(3), 351–375 (2019)

    Article  Google Scholar 

  19. Do, M.T., Yoon, S., Hooi, B., Shin, K.: Structural patterns and generative models of real-world hypergraphs. In: KDD ’20: The 26th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pp. 176–186. ACM (2020)

  20. Fang, Y., Yu, K., Cheng, R., Lakshmanan, L.V.S., Lin, X.: Efficient algorithms for densest subgraph discovery. Proc. VLDB Endow. 12(11), 1719–1732 (2019)

    Article  Google Scholar 

  21. Fatemi, B., Taslakian, P., Vázquez, D., Poole, D.: Knowledge hypergraphs: extending knowledge graphs beyond binary relations. CoRR abs/1906.00137 (2019)

  22. Feng, Y., You, H., Zhang, Z., Ji, R., Gao, Y.: Hypergraph neural networks. In: The Thirty-First Innovative Applications of Artificial Intelligence Conference, pp. 3558–3565. AAAI Press (2019)

  23. 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. IEEE (2021). https://doi.org/10.1109/IPDPSW52791.2021.00158

  24. Gabert, K., Pinar, A., Çatalyürek, Ü.V.: A unifying framework to identify dense subgraphs on streams: graph nuclei to hypergraph cores. In: WSDM ’21, The Fourteenth ACM International Conference on Web Search and Data Mining, pp. 689–697. ACM (2021). https://doi.org/10.1145/3437963.3441790

  25. Gabert, K., Pinar, A., Çatalyürek, Ü.V.: A unifying framework to identify dense subgraphs on streams: graph nuclei to hypergraph cores. In: WSDM ’21, The Fourteenth ACM International Conference on Web Search and Data Mining, pp. 689–697. ACM (2021). https://doi.org/10.1145/3437963.3441790

  26. Gionis, A., Tsourakakis, C.E.: Dense subgraph discovery: KDD 2015 tutorial. In: Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 2313–2314. ACM (2015)

  27. Hu, S., Wu, X., Chan, T.H.: Maintaining densest subsets efficiently in evolving hypergraphs. In: Proceedings of Conference on Information and Knowledge Management, CIKM, pp. 929–938. ACM (2017)

  28. 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 

  29. Huang, J., Zhang, R., Yu, J.X.: Scalable hypergraph learning and processing. In: 2015 IEEE International Conference on Data Mining, ICDM, pp. 775–780. IEEE Computer Society (2015)

  30. Huang, X., Cheng, H., Qin, L., Tian, W., Yu, J.X.: Querying k-truss community in large and dynamic graphs. In: International Conference on Management of Data, SIGMOD, pp. 1311–1322. ACM (2014). https://doi.org/10.1145/2588555.2610495

  31. Hwang, T., Tian, Z., Kuang, R., Kocher, J.A.: Learning on weighted hypergraphs to integrate protein interactions and gene expressions for cancer outcome prediction. In: Proceedings of the 8th IEEE International Conference on Data Mining ICDM, pp. 293–302. (2008)

  32. Jiang, J., Mitzenmacher, M., Thaler, J.: Parallel peeling algorithms. ACM Trans. Parallel Comput. 3(1), 7:1-7:27 (2016)

    Article  Google Scholar 

  33. 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 Distrib. Syst. 29(11), 2416–2428 (2018)

    Article  Google Scholar 

  34. Karypis, G., Aggarwal, R., Kumar, V., Shekhar, S.: Multilevel hypergraph partitioning: applications in VLSI domain. IEEE Trans. Very Large Scale Integr. Syst. 7(1), 69–79 (1999)

    Article  Google Scholar 

  35. Kwak, H., Lee, C., Park, H., Moon, S.B.: What is twitter, a social network or a news media? In: Proceedings of the 19th International Conference on World Wide Web, WWW, pp. 591–600. ACM (2010). https://doi.org/10.1145/1772690.1772751

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

    Article  Google Scholar 

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

    Google Scholar 

  38. Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: 22nd International World Wide Web Conference, WWW Companion Volume, pp. 41–42. International World Wide Web Conferences Steering Committee/ACM (2013)

  39. Li, J., He, J., Zhu, Y.: E-tail product return prediction via hypergraph-based local graph cut. In: Y. Guo, F. Farooq (eds.) Proceedings of the 24th ACM International Conference on Knowledge Discovery & Data Mining, KDD, pp. 519–527. ACM (2018)

  40. Li, R., Qin, L., Ye, F., Yu, J.X., Xiao, X., Xiao, N., Zheng, Z.: Skyline community search in multi-valued networks. In: Proceedings of the 2018 International Conference on Management of Data, SIGMOD, pp. 457–472. ACM (2018). https://doi.org/10.1145/3183713.3183736

  41. Lin, J.H., Guo, Q., Dong, W., ying Tang, L., Liu, J.: Identifying the node spreading influence with largest k-core values. Phys. Lett. A 378, 3279–3284 (2014)

    Article  MATH  Google Scholar 

  42. Liu, Q., Huang, Y., Metaxas, D.N.: Hypergraph with sampling for image retrieval. Pattern Recogn. 44(10–11), 2255–2262 (2011)

    Article  MATH  Google Scholar 

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

  44. Luo, Q., Yu, D., Cheng, X., Cai, Z., Yu, J., Lv, W.: Batch processing for truss maintenance in large dynamic graphs. IEEE Trans. Comput. Soc. Syst. 7(6), 1435–1446 (2020). https://doi.org/10.1109/TCSS.2020.3026574

    Article  Google Scholar 

  45. 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, vol. 11917, pp. 16–32. Springer, Ho Chi Minh City, Vietnam (2019)

    Google Scholar 

  46. 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 

  47. Ouyang, M., Toulouse, M., Thulasiraman, K., Glover, F.W., Deogun, J.S.: Multilevel cooperative search for the circuit/hypergraphpartitioning problem. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 21(6), 685–693 (2002)

    Article  Google Scholar 

  48. Preti, G., Morales, G.D.F., Bonchi, F.: Strud: Truss decomposition of simplicial complexes. In: WWW ’21: The Web Conference 2021, pp. 3408–3418. ACM/IW3C2 (2021). https://doi.org/10.1145/3442381.3450073

  49. 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 

  50. Sariyüce, A.E., Seshadhri, C., Pinar, A., Çatalyürek, Ü.V.: Finding the hierarchy of dense subgraphs using nucleus decompositions. In: Proceedings of the 24th International Conference on World Wide Web, pp. 927–937. ACM (2015). https://doi.org/10.1145/2736277.2741640

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

    Article  MathSciNet  Google Scholar 

  52. 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. IEEE Computer Society. https://doi.org/10.1109/ICDM.2016.0058

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

  54. Sun, B., Chan, T.H., Sozio, M.: Fully dynamic approximate k-core decomposition in hypergraphs. ACM Trans. Knowl. Discov. Data 14(4), 39:1-39:21 (2020)

    Article  Google Scholar 

  55. Tan, H., Ngo, C., Wu, X.: Modeling video hyperlinks with hypergraph for web video reranking. In: Proceedings of the 16th International Conference on Multimedia, pp. 659–662. ACM (2008)

  56. Tan, S., Guan, Z., Cai, D., Qin, X., Bu, J., Chen, C.: Mapping users across networks by manifold alignment on hypergraph. In: Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence, pp. 159–165. AAAI Press (2014)

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

  58. Tsourakakis, C.E., Bonchi, F., Gionis, A., Gullo, F., Tsiarli, M.A.: Denser than the densest subgraph: extracting optimal quasi-cliques with quality guarantees. In: The 19th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 104–112. ACM (2013)

  59. Wang, J., Cheng, J.: Truss decomposition in massive networks. Proc. VLDB Endow. 5(9), 812–823 (2012). https://doi.org/10.14778/2311906.2311909

    Article  Google Scholar 

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

  61. 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)

  62. Yang, D., Qu, B., Yang, J., Cudré-Mauroux, P.: Revisiting user mobility and social relationships in lbsns: A hypergraph embedding approach. In: The World Wide Web Conference, WWW, pp. 2147–2157. ACM (2019)

  63. Yu, D., Zhang, L., Luo, Q., Cheng, X., Yu, J., Cai, Z.: Fast skyline community search in multi-valued networks. Big Data Min. Anal. 3(3), 171–180 (2020). https://doi.org/10.26599/BDMA.2020.9020002

    Article  Google Scholar 

  64. Yuan, L., Qin, L., Lin, X., Chang, L., Zhang, W.: I/O efficient ECC graph decomposition via graph reduction. VLDB J. 26(2), 275–300 (2017). https://doi.org/10.1007/s00778-016-0451-4

    Article  Google Scholar 

  65. Zhang, M., Cui, Z., Jiang, S., Chen, Y.: Beyond link prediction: Predicting hyperlinks in adjacency space. In: Proceedings of the Thirty-Second AAAI Conference on Artificial Intelligence, pp. 4430–4437. AAAI Press (2018)

  66. Zheng, X., Luo, Y., Sun, L., Ding, X., Zhang, J.: A novel social network hybrid recommender system based on hypergraph topologic structure. World Wide Web 21(4), 985–1013 (2018)

    Article  Google Scholar 

  67. Zhou, D., Huang, J., Schölkopf, B.: Learning with hypergraphs: Clustering, classification, and embedding. In: Proceedings of the Twentieth Annual Conference on Neural Information Processing Systems, pp. 1601–1608. MIT Press (2006)

  68. Zhu, Y., Guan, Z., Tan, S., Liu, H., Cai, D., He, X.: Heterogeneous hypergraph embedding for document recommendation. Neurocomputing 216, 150–162 (2016)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported in part by the National Key Research and Development Program of China under Grant 2020YFB1005900, in part by National Natural Science Foundation of China (NSFC) under Grant 62122042, and in part by Shandong University multidisciplinary research and innovation team of young scholars under Grant 2020QNQT017. Dongxiao Yu is the corresponding author of this work.

Author information

Authors and Affiliations

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

    Qi Luo, Dongxiao Yu & Xiuzhen Cheng

  2. Department of Computing Science, Georgia State University, Atlanta, USA

    Zhipeng Cai

  3. School of Computer Science and Engineering, University of New South Wales, Sydney, Australia

    Xuemin Lin

  4. School of Mathematics, Shandong University, Jinan, People’s Republic of China

    Guanghui Wang

Authors
  1. Qi Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dongxiao Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhipeng Cai
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xuemin Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Guanghui Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Xiuzhen Cheng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dongxiao Yu.

Additional information

Publisher's Note

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

A preliminary version of this work has been accepted by ICDE 2021 as a short paper.

Rights and permissions

Springer Nature or its licensor 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. Toward maintenance of hypercores in large-scale dynamic hypergraphs. The VLDB Journal 32, 647–664 (2023). https://doi.org/10.1007/s00778-022-00763-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00778-022-00763-z

Keywords

Search

Navigation