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ForGen: Autoregressive Generation of Sparse Graphs with Preferential Forest

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Web and Big Data (APWeb-WAIM 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13421))

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Abstract

Graph is a natural way to model interactions between objects, such as in the field of biology and social science. Over the past decades, modeling and generating graphs have been a popular research topic, largely inspired by observed properties of real-world graphs. Since traditional approaches relying on hand-crafted mechanisms are only capable of capturing some specific graph properties, recent focus has been shifted to deep neural methods. However, the task is still challenging in terms of efficiency. To address this issue, we observe that the connectivity (i.e., degree) of nodes follows scale-free distribution for most real-world graphs, which can be utilized to accelerate the generation process. We propose ForGen, a Forest-based Generation model that contains a graph-level and an edge-level autoregressive generator. Specifically, for the edge-level model, motivated by the skewed distribution of node degree and the Huffman tree, we design a forest-like data structure to accelerate edge connection via shallow tree searches and better parallelism. Experiments on both synthetic and real-world graph datasets show that ForGen is two times faster than the current state-of-the-art method for graph generation, and guarantees better generated graph quality.

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Notes

  1. 1.

    https://github.com/snap-stanford/GraphRNN.

  2. 2.

    https://github.com/lrjconan/GRAN.

  3. 3.

    https://github.com/google-research/google-research/tree/master/bigg.

References

  1. Albert, R., Barabási, A.L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74(1), 47 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  2. Barabási, A.: Network Science. Cambridge University , Cambridge (2016)

    Google Scholar 

  3. Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)

    Google Scholar 

  4. Dai, H., Nazi, A., Li, Y., Dai, B., Schuurmans, D.: Scalable deep generative modeling for sparse graphs. In: International Conference on Machine Learning, pp. 2302–2312. PMLR (2020)

    Google Scholar 

  5. Erdos, P., Rényi, A., et al.: On the evolution of random graphs. Publ. Math. Inst. Hung. Acad. Sci 5(1), 17–60 (1960)

    MathSciNet  MATH  Google Scholar 

  6. Fenwick, P.M.: A new data structure for cumulative frequency tables. Softw. Pract. Exp. 24(3), 327–336 (1994)

    Google Scholar 

  7. Goyal, N., Jain, H.V., Ranu, S.: Graphgen: a scalable approach to domain-agnostic labeled graph generation. In: Proceedings of The Web Conference 2020, pp. 1253–1263 (2020)

    Google Scholar 

  8. Grover, A., Zweig, A., Ermon, S.: Graphite: iterative generative modeling of graphs. In: International Conference on Machine Learning, pp. 2434–2444. PMLR (2019)

    Google Scholar 

  9. Guo, X., Zhao, L.: A systematic survey on deep generative models for graph generation. arXiv preprint arXiv:2007.06686 (2020)

  10. Huffman, D.A.: A method for the construction of minimum-redundancy codes. Proc. IRE 40(9), 1098–1101 (1952)

    Article  MATH  Google Scholar 

  11. Jeong, H., Néda, Z., Barabási, A.L.: Measuring preferential attachment in evolving networks. EPL (Europhys. Lett.) 61(4), 567 (2003)

    Article  Google Scholar 

  12. Kunegis, J.: KONECT - The Koblenz network collection. In: Proceedings International Conference on World Wide Web Companion, pp. 1343–1350 (2013)

    Google Scholar 

  13. Kunegis, J., Blattner, M., Moser, C.: Preferential attachment in online networks: measurement and explanations. In: Proceedings of the 5th Annual ACM Web Science Conference, pp. 205–214 (2013)

    Google Scholar 

  14. Leskovec, J., Chakrabarti, D., Kleinberg, J., Faloutsos, C., Ghahramani, Z.: Kronecker graphs: an approach to modeling networks. J. Mach. Learn. Res. 11(2) (2010)

    Google Scholar 

  15. Leskovec, J., Kleinberg, J., Faloutsos, C.: Graphs over time: densification laws, shrinking diameters and possible explanations. In: Proceedings of the Eleventh ACM SIGKDD International Conference on Knowledge Discovery in Data Mining, pp. 177–187 (2005)

    Google Scholar 

  16. Li, Y., Zhang, L., Liu, Z.: Multi-objective de novo drug design with conditional graph generative model. J. Cheminform. 10(1), 1–24 (2018). https://doi.org/10.1186/s13321-018-0287-6

    Article  Google Scholar 

  17. Liao, R., et al.: Efficient graph generation with graph recurrent attention networks. In: Proceedings of the 33rd International Conference on Neural Information Processing Systems, pp. 4255–4265 (2019)

    Google Scholar 

  18. Liu, C.C., Chan, H., Luk, K., Borealis, A.: Auto-regressive graph generation modeling with improved evaluation methods. In: Proceedings of NeurIPS Workshop Graph Representation Learning (2019)

    Google Scholar 

  19. Price, D.J.D.S.: Networks of scientific papers. Science, 510–515 (1965)

    Google Scholar 

  20. Simonovsky, M., Komodakis, N.: GraphVAE: towards generation of small graphs using variational autoencoders. In: Kůrková, V., Manolopoulos, Y., Hammer, B., Iliadis, L., Maglogiannis, I. (eds.) ICANN 2018. LNCS, vol. 11139, pp. 412–422. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-01418-6_41

    Chapter  Google Scholar 

  21. Snijders, T.A., Nowicki, K.: Estimation and prediction for stochastic blockmodels for graphs with latent block structure. J. Classif. 14(1), 75–100 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  22. Tai, K.S., Socher, R., Manning, C.D.: Improved semantic representations from tree-structured long short-term memory networks. In: ACL, no. 1 (2015)

    Google Scholar 

  23. Tuteja, S., Kumar, R.: A unification of heterogeneous data sources into a graph model in e-commerce. Data Sci. Eng. 7(1), 57–70 (2022)

    Article  Google Scholar 

  24. Vaswani, A., et al.: Attention is all you need. In: Advances in Neural Information Processing Systems, pp. 5998–6008 (2017)

    Google Scholar 

  25. Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393(6684), 440–442 (1998)

    Google Scholar 

  26. Xiao, H., Huang, M., Zhu, X.: TransG: a generative model for knowledge graph embedding. In: Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pp. 2316–2325 (2016)

    Google Scholar 

  27. Xie, S., Kirillov, A., Girshick, R., He, K.: Exploring randomly wired neural networks for image recognition. In: Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 1284–1293 (2019)

    Google Scholar 

  28. Yi, P., Li, J., Choi, B., Bhowmick, S.S., Xu, J.: Flag: Towards graph query autocompletion for large graphs. Data Sci. Eng. 7(2), 175–191 (2022)

    Article  Google Scholar 

  29. You, J., Liu, B., Ying, R., Pande, V., Leskovec, J.: Graph convolutional policy network for goal-directed molecular graph generation. In: Proceedings of the 32nd International Conference on Neural Information Processing Systems, pp. 6412–6422 (2018)

    Google Scholar 

  30. You, J., Ying, R., Ren, X., Hamilton, W., Leskovec, J.: GraphRNN: generating realistic graphs with deep auto-regressive models. In: International Conference on Machine Learning, pp. 5708–5717. PMLR (2018)

    Google Scholar 

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Authors and Affiliations

  1. Peking University, Beijing, China

    Yao Shi, Yu Liu & Lei Zou

Authors
  1. Yao Shi
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  2. Yu Liu
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  3. Lei Zou
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Corresponding author

Correspondence to Yao Shi .

Editor information

Editors and Affiliations

  1. Nanjing University of Aeronautics and Astronautics, Nanjing, China

    Bohan Li

  2. Newcastle University, Callaghan, NSW, Australia

    Lin Yue

  3. Nanjing University of Aeronautics and Astronautics, Nanjing, China

    Chuanqi Tao

  4. Jinan University, Guangzhou, China

    Xuming Han

  5. Free University of Bozen-Bolzano, Bolzano, Italy

    Diego Calvanese

  6. University of Tsukuba, Tsukuba, Japan

    Toshiyuki Amagasa

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Shi, Y., Liu, Y., Zou, L. (2023). ForGen: Autoregressive Generation of Sparse Graphs with Preferential Forest. In: Li, B., Yue, L., Tao, C., Han, X., Calvanese, D., Amagasa, T. (eds) Web and Big Data. APWeb-WAIM 2022. Lecture Notes in Computer Science, vol 13421. Springer, Cham. https://doi.org/10.1007/978-3-031-25158-0_40

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  • DOI: https://doi.org/10.1007/978-3-031-25158-0_40

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-25157-3

  • Online ISBN: 978-3-031-25158-0

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