Skip to main content
SpringerLink
Log in

Kinematic-Based Force-Directed Graph Embedding

  • Conference paper
  • First Online:
Complex Networks XV (CompleNet-Live 2024)

Part of the book series: Springer Proceedings in Complexity ((SPCOM))

Included in the following conference series:

  • 62 Accesses

Abstract

Graph embedding has become an increasingly important technique for analyzing graph-structured data. By representing nodes in a graph as vectors in a low-dimensional space, graph embedding enables efficient graph processing and analysis tasks like node classification, link prediction, and visualization. In this paper, we propose and provide proof of convergence for a novel graph embedding paradigm where nodes are assumed to possess mass and a kinematic-based force-directed model is applied to calculate embedding gradients. Our proposed force-directed graph embedding method utilizes the steady acceleration kinematic equations to embed nodes in a way that preserves graph topology and structural features. This method simulates a set of customized attractive and repulsive forces between all node pairs with respect to their hop distance. These forces are then used in Newton’s second law to obtain the acceleration of each node. The method is intuitive, parallelizable, and highly scalable. We evaluate our method on several graph analysis tasks and show that it achieves competitive performance compared to state-of-the-art unsupervised embedding techniques.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    https://github.com/thunlp/MMDW accessed on July 28.2023.

References

  1. Lotfalizadeh, H., Al Hasan, M.: Force-directed graph embedding with hops distance. In: 2023 IEEE International Conference on Big Data (Big Data). IEEE (2023)

    Google Scholar 

  2. Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500), 2323–2326 (2000)

    Google Scholar 

  3. Belkin, Mikhail, Niyogi, Partha: Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput. 15(6), 1373–1396 (2003)

    Article  Google Scholar 

  4. Tang, J., Qu, M., Wang, M., Zhang, M., Yan, J., Mei, Q.:. Line: Large-scale information network embedding. In: Proceedings of the 24th International Conference on World Wide Web, pp. 1067–1077 (2015)

    Google Scholar 

  5. Wang, D., Cui, P., Zhu, W.: Structural deep network embedding. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1225–1234 (2016)

    Google Scholar 

  6. Perozzi, R.A-R., Skiena, S.: Deepwalk: online learning of social representations. In: Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 701–710 (2014)

    Google Scholar 

  7. Grover, A., Leskovec, J.: node2vec: Scalable feature learning for networks. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 855–864 (2016)

    Google Scholar 

  8. Mikolov, T., Sutskever, I., Chen, K., Corrado, G.S., Dean, J.: Distributed representations of words and phrases and their compositionality. Advances in Neural Information Processing Systems, vol. 26 (2013)

    Google Scholar 

  9. Kamada, Tomihisa, Kawai, Satoru, et al.: An algorithm for drawing general undirected graphs. Inf. Process. Lett. 31(1), 7–15 (1989)

    Article  MathSciNet  Google Scholar 

  10. Fruchterman, T.M.J., Reingold, E.M.: Graph drawing by force-directed placement. Softw.: Pract. Exp. 21(11), 1129–1164 (1991)

    Google Scholar 

  11. Walshaw, C.: A multilevel algorithm for force-directed graph drawing. In: Graph Drawing: 8th International Symposium, GD 2000 Colonial Williamsburg, VA, USA, September 20–23, 2000 Proceedings 8, pp. 171–182. Springer (2001)

    Google Scholar 

  12. Gajer, P., Goodrich, M.T., Kobourov, S.G.: A multi-dimensional approach to force-directed layouts of large graphs. In: International Symposium on Graph Drawing, pp. 211–221. Springer (2000)

    Google Scholar 

  13. Eades, P., Huang, M.L.: Navigating clustered graphs using force-directed methods. In: Graph Algorithms And Applications, vol. 2, pp. 191–215. World Scientific (2004)

    Google Scholar 

  14. Yifan, Hu.: Efficient, high-quality force-directed graph drawing. Mathematica journal 10(1), 37–71 (2005)

    MathSciNet  Google Scholar 

  15. Danny Holten and Jarke J Van Wijk. Force-directed edge bundling for graph visualization. In Computer graphics forum, volume 28, pages 983–990. Wiley Online Library, 2009

    Google Scholar 

  16. Stephen G Kobourov. Spring embedders and force directed graph drawing algorithms. arXiv preprint arXiv:1201.3011, 2012

  17. Michael J Bannister, David Eppstein, Michael T Goodrich, and Lowell Trott. Force-directed graph drawing using social gravity and scaling. In Graph Drawing: 20th International Symposium, GD 2012, Redmond, WA, USA, September 19-21, 2012, Revised Selected Papers 20, pages 414–425. Springer, 2013

    Google Scholar 

  18. Md Khaledur Rahman, Majedul Haque Sujon, and Ariful Azad. Force2vec: Parallel force-directed graph embedding. In 2020 IEEE International Conference on Data Mining (ICDM), pages 442–451. IEEE, 2020

    Google Scholar 

  19. Md Khaledur Rahman, Majedul Haque Sujon, and Ariful Azad. Scalable force-directed graph representation learning and visualization. Knowledge and Information Systems, 64(1):207–233, 2022

    Google Scholar 

  20. Park, Sehie: Ninety years of the brouwer fixed point theorem. Vietnam J. Math. 27(3), 187–222 (1999)

    MathSciNet  Google Scholar 

  21. Lars Buitinck, Gilles Louppe, Mathieu Blondel, Fabian Pedregosa, Andreas Mueller, Olivier Grisel, Vlad Niculae, Peter Prettenhofer, Alexandre Gramfort, Jaques Grobler, Robert Layton, Jake VanderPlas, Arnaud Joly, Brian Holt, and Gaël Varoquaux. API design for machine learning software: experiences from the scikit-learn project. In ECML PKDD Workshop: Languages for Data Mining and Machine Learning, pages 108–122, 2013

    Google Scholar 

  22. Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M., Duchesnay, E.: Scikit-learn: Machine learning in Python. J. Mach. Learn. Res. 12, 2825–2830 (2011)

    MathSciNet  Google Scholar 

  23. Sen, Prithviraj, Namata, Galileo, Bilgic, Mustafa, Getoor, Lise, Galligher, Brian, Eliassi-Rad, Tina: Collective classification in network data. AI Mag. 29(3), 93–93 (2008)

    Google Scholar 

  24. Galileo Namata, Ben London, Lise Getoor, Bert Huang, and U Edu. Query-driven active surveying for collective classification. In 10th international workshop on mining and learning with graphs, volume 8, page 1, 2012

    Google Scholar 

  25. Jure Leskovec and Julian Mcauley. Learning to discover social circles in ego networks. Advances in neural information processing systems, 25, 2012

    Google Scholar 

  26. Aleksandar Bojchevski and Stephan Günnemann. Deep gaussian embedding of graphs: Unsupervised inductive learning via ranking. arXiv preprint arXiv:1707.03815, 2017

Download references

Author information

Authors and Affiliations

  1. Purdue University, West Lafayette, IN, USA

    Hamidreza Lotfalizadeh

  2. Luddy School of Informatics, Computing, and Engineering: IUPUI, Indianapolis, IN, USA

    Mohammad Al Hasan

Authors
  1. Hamidreza Lotfalizadeh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohammad Al Hasan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hamidreza Lotfalizadeh .

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Exeter, Exeter, UK

    Federico Botta

  2. Department of Data Science, Northeastern University London, London, UK

    Mariana Macedo

  3. Department of Computer Science, University of Exeter, Exeter, UK

    Hugo Barbosa

  4. Department of Computer Science, University of Exeter, Exeter, UK

    Ronaldo Menezes

Rights and permissions

Reprints and permissions

Copyright information

© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Lotfalizadeh, H., Hasan, M.A. (2024). Kinematic-Based Force-Directed Graph Embedding. In: Botta, F., Macedo, M., Barbosa, H., Menezes, R. (eds) Complex Networks XV. CompleNet-Live 2024. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-031-57515-0_11

Download citation

Publish with us

Policies and ethics

Search

Navigation