Skip to main content

Correcting Output Degree Sequences in Chung-Lu Random Graph Generation

  • Conference paper
  • First Online:
Complex Networks and Their Applications XI (COMPLEX NETWORKS 2016 2022)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 1078))

Included in the following conference series:

Abstract

Random graphs play a central role in network analysis. The Chung-Lu random graph model is one particularly popular model, which connects nodes according to their desired degrees to form a specific degree distribution in expectation. Despite its popularity, the standard Chung-Lu graph generation algorithms are susceptible to significant degree sequence errors when generating simple graphs. In this manuscript, we suggest multiple methods for improving the accuracy of Chung-Lu graph generation by computing node weights which better recreate the desired output degree sequence. We show that each of our solutions offer a significant improvement in degree sequence accuracy.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 349.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 449.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 449.99
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://snap.stanford.edu/data/.

References

  1. Alam, M., Khan, M., Vullikanti, A., Marathe, M.: An efficient and scalable algorithmic method for generating large-scale random graphs. In: SC’16: Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis. pp. 372–383. IEEE (2016)

    Google Scholar 

  2. Batagelj, V., Brandes, U.: Efficient generation of large random networks. Phys. Rev. E 71(3), 036113 (2005)

    Article  Google Scholar 

  3. Bollobás, B.: A probabilistic proof of an asymptotic formula for the number of labelled regular graphs. Euro. J. Combin. 1(4), 311–316 (1980)

    Article  MATH  Google Scholar 

  4. Bonnans, J.F., Gilbert, J.C., Lemaréchal, C., Sagastizábal, C.A.: Numerical Optimization: Theoretical and Practical Aspects. Springer Science & Business Media (2006)

    Google Scholar 

  5. Brissette, C., Slota, G.M.: Limitations of Chung Lu random graph generation. In: International Conference on Complex Networks and Their Applications. pp. 451–462. Springer (2021)

    Google Scholar 

  6. Chung, F., Lu, L.: The average distances in random graphs with given expected degrees. Proc. Nat. Acad. Sci. 99(25), 15879–15882 (2002)

    Article  MATH  Google Scholar 

  7. Drobyshevskiy, M., Turdakov, D.: Random graph modeling: a survey of the concepts. ACM Comput. Surveys (CSUR) 52(6), 1–36 (2019)

    Article  Google Scholar 

  8. Durak, N., Kolda, T.G., Pinar, A., Seshadhri, C.: A scalable null model for directed graphs matching all degree distributions: in, out, and reciprocal. In: 2013 IEEE 2nd Network Science Workshop (NSW). pp. 23–30. IEEE (2013)

    Google Scholar 

  9. Fosdick, B.K., Larremore, D.B., Nishimura, J., Ugander, J.: Configuring random graph models with fixed degree sequences. SIAM Rev. 60(2), 315–355 (2018)

    Article  MATH  Google Scholar 

  10. Garbus, J., Brissette, C., Slota, G.M.: Parallel generation of simple null graph models. In: The 5th IEEE Workshop on Parallel and Distributed Processing for Computational Social Systems (ParSocial) (2020)

    Google Scholar 

  11. Hagberg, A., Swart, P., S Chult, D.: Exploring network structure, dynamics, and function using network. Tech. rep., Los Alamos National Lab. (LANL), Los Alamos, NM (United States) (2008)

    Google Scholar 

  12. Holland, P.W., Laskey, K.B., Leinhardt, S.: Stochastic blockmodels: first steps. Soc. Netw. 5(2), 109–137 (1983)

    Article  Google Scholar 

  13. Kolda, T.G., Pinar, A., Plantenga, T., Seshadhri, C.: A scalable generative graph model with community structure. SIAM J. Sci. Comput. 36(5), C424–C452 (2014)

    Article  MATH  Google Scholar 

  14. Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii, D., Alon, U.: Network motifs: simple building blocks of complex networks. Science 298(5594), 824–827 (2002)

    Article  Google Scholar 

  15. Molloy, M., Reed, B.: A critical point for random graphs with a given degree sequence. Random Struct. Algorithms 6(2–3), 161–180 (1995)

    Article  MATH  Google Scholar 

  16. Newman, M.E.: Modularity and community structure in networks. Proc. Nat. Acad. Sci. 103(23), 8577–8582 (2006)

    Article  Google Scholar 

  17. Slota, G.M., Berry, J., Hammond, S.D., Olivier, S., Phillips, C., Rajamanickam, S.: Scalable generation of graphs for benchmarking HPC community-detection algorithms. In: IEEE International Conference for High Performance Computing, Networking, Storage and Analysis (SC) (2019)

    Google Scholar 

  18. Slota, G.M., Garbus, J.: A parallel LFR-like benchmark for evaluating community detection algorithms. In: The 5th IEEE Workshop on Parallel and Distributed Processing for Computational Social Systems (ParSocial) (2020)

    Google Scholar 

  19. Winlaw, M., DeSterck, H., Sanders, G.: An in-depth analysis of the Chung-Lu model. Tech. rep., Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States) (2015)

    Google Scholar 

  20. Zaki, M.J., Meira Jr, W., Meira, W.: Data Mining and Analysis: Fundamental Concepts and Algorithms. Cambridge University Press (2014)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Christopher Brissette .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2023 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

Brissette, C., Liu, D., Slota, G.M. (2023). Correcting Output Degree Sequences in Chung-Lu Random Graph Generation. In: Cherifi, H., Mantegna, R.N., Rocha, L.M., Cherifi, C., Micciche, S. (eds) Complex Networks and Their Applications XI. COMPLEX NETWORKS 2016 2022. Studies in Computational Intelligence, vol 1078. Springer, Cham. https://doi.org/10.1007/978-3-031-21131-7_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-21131-7_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-21130-0

  • Online ISBN: 978-3-031-21131-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics