Skip to main content

Modularity-Based Backbone Extraction in Weighted Complex Networks

  • Conference paper
  • First Online:
Network Science (NetSci-X 2022)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 13197))

Included in the following conference series:

Abstract

The constantly growing size of real-world networks is a great challenge. Therefore, building a compact version of networks allowing their analyses is a must. Backbone extraction techniques are among the leading solutions to reduce network size while preserving its features. Coarse-graining merges similar nodes to reduce the network size, while filter-based methods remove nodes or edges according to a specific statistical property. Since community structure is ubiquitous in real-world networks, preserving it in the backbone extraction process is of prime interest. To this end, we propose a filter-based method. The so-called “modularity vitality backbone” removes nodes with the lower contribution to the network’s modularity. Experimental results show that the proposed strategy outperforms the “overlapping nodes ego backbone” and the “overlapping nodes and hub backbone.” These two backbone extraction processes recently introduced have proved their efficacy to preserve better the information of the original network than the popular disparity filter.

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 44.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Similar content being viewed by others

Notes

  1. 1.

    Aaron Clauset, Ellen Tucker, and Matthias Sainz, “The Colorado Index of Complex Networks.” https://icon.colorado.edu/ (2016).

  2. 2.

    Tiago P. Peixoto, “The Netzschleuder network catalogue and repository,” https://networks.skewed.de/ (2020).

References

  1. Zeng, A., Lü, L.: Coarse graining for synchronization in directed networks. Phys. Rev. E 83(5), 056123 (2011)

    Article  Google Scholar 

  2. Zeng, L., Jia, Z., Wang, Y.: A new spectral coarse-graining algorithm based on k-means clustering in complex networks. Mod. Phys. Lett. B 33(01), 1850421 (2019)

    Article  Google Scholar 

  3. Coscia, M., Neffke, F.: Network backboning with noisy data. In: International Conference on Data Engineering (ICDE) (2017)

    Google Scholar 

  4. Simas, T., Correia, R.B., Rocha, L.M.: The distance backbone of complex networks. J. Complex Netw. 9(6), cnab021 (2021)

    Article  MathSciNet  Google Scholar 

  5. Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., Hwang, D.-U.: Complex networks: structure and dynamics. Phys. Rep. 424(4–5), 175–308 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. Jebabli, M., Cherifi, H., Cherifi, C., Hamouda, A.: Community detection algorithm evaluation with ground-truth data. Physica A Stat. Mech. Appl. 492, 651–706 (2018)

    Article  Google Scholar 

  7. Peel, L., Schaub, M.T.: Detectability of hierarchical communities in networks. arXiv preprint arXiv:2009.07525 (2020)

  8. Atzmueller, M., Günnemann, S., Zimmermann, A.: Mining communities and their descriptions on attributed graphs: a survey. Data Min. Knowl. Disc. 35(3), 661–687 (2021). https://doi.org/10.1007/s10618-021-00741-z

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  10. Ghalmane, Z., Cherifi, C., Cherifi, H., El Hassouni, M.: Extracting backbones in weighted modular complex networks. Sci. Rep. 10(1), 1–18 (2020)

    Article  Google Scholar 

  11. Ghalmane, Z., Cherifi, C., Cherifi, H., El Hassouni, M.: Extracting modular-based backbones in weighted networks. Inf. Sci. 576, 454–474 (2021)

    Article  MathSciNet  Google Scholar 

  12. Van Den Heuvel, M.P., Kahn, R.S., Goñi, J., Sporns, O.: High-cost, high-capacity backbone for global brain communication. Proc. Natl. Acad. Sci. 109(28), 11372–11377 (2012)

    Article  Google Scholar 

  13. Cao, J., Ding, C., Shi, B.: Motif-based functional backbone extraction of complex networks. Physica A Stat. Mech. Appl. 526, 121123 (2019)

    Article  Google Scholar 

  14. Katharina Anna Zweig and Michael Kaufmann: A systematic approach to the one-mode projection of bipartite graphs. Soc. Netw. Anal. Min. 1(3), 187–218 (2011)

    Article  Google Scholar 

  15. Neal, Z.: Identifying statistically significant edges in one-mode projections. Soc. Netw. Anal. Min. 3(4), 915–924 (2013). https://doi.org/10.1007/s13278-013-0107-y

    Article  Google Scholar 

  16. Neal, Z.: The backbone of bipartite projections: inferring relationships from co-authorship, co-sponsorship, co-attendance and other co-behaviors. Soc. Netw. 39, 84–97 (2014)

    Article  Google Scholar 

  17. Gfeller, D., De Los Rios, P.: Spectral coarse graining of complex networks. Phys. Rev. Lett. 99(3), 038701 (2007)

    Google Scholar 

  18. Chen, M., Li, L., Wang, B., Cheng, J., Pan, L., Chen, X.: Effectively clustering by finding density backbone based-on KNN. Pattern Recogn. 60, 486–498 (2016)

    Article  Google Scholar 

  19. Serrano, M.Á., Boguná, M., Vespignani, A.: Extracting the multiscale backbone of complex weighted networks. Proc. Natl. Acad. Sci. 106(16), 6483–6488 (2009)

    Article  Google Scholar 

  20. Goh, K.-I., Salvi, G., Kahng, B., Kim, D.: Skeleton and fractal scaling in complex networks. Phys. Rev. Lett. 96(1), 018701 (2006)

    Article  Google Scholar 

  21. Zhang, R.J., Stanley, H.E., Fred, Y.Y.: Extracting h-backbone as a core structure in weighted networks. Sci. Rep. 8(1), 1–7 (2018)

    Google Scholar 

  22. Dai, L., Derudder, B., Liu, X.: Transport network backbone extraction: a comparison of techniques. J. Transp. Geogr. 69, 271–281 (2018)

    Article  Google Scholar 

  23. Malang, K., Wang, S., Lv, Y., Phaphuangwittayakul, A.: Skeleton network extraction and analysis on bicycle sharing networks. Int. J. Data Warehouse. Min. (IJDWM) 16(3), 146–167 (2020)

    Article  Google Scholar 

  24. Koschützki, D., Lehmann, K.A., Peeters, L., Richter, S., Tenfelde-Podehl, D., Zlotowski, O.: Centrality indices. In: Brandes, U., Erlebach, T. (eds.) Network Analysis. LNCS, vol. 3418, pp. 16–61. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-31955-9_3

    Chapter  Google Scholar 

  25. Yang, J., Leskovec, J.: Defining and evaluating network communities based on ground-truth. Knowl. Inf. Syst. 42(1), 181–213 (2013). https://doi.org/10.1007/s10115-013-0693-z

    Article  Google Scholar 

  26. Leskovec, J., Lang, K.J., Mahoney, M.: Empirical comparison of algorithms for network community detection. In: Proceedings of the 19th International Conference on World Wide Web, pp. 631–640 (2010)

    Google Scholar 

  27. Rajeh, S., Savonnet, M., Leclercq, E., Cherifi, H.: Characterizing the interactions between classical and community-aware centrality measures in complex networks. Sci. Rep. 11(1), 1–15 (2021)

    Article  Google Scholar 

  28. Clauset, A., Newman, M.E.J., Moore, C.: Finding community structure in very large networks. Phys. Rev. E 70(6), 066111 (2004)

    Article  Google Scholar 

  29. Brandes, U., et al.: On modularity clustering. IEEE Trans. Knowl. Data Eng. 20(2), 172–188 (2007)

    Article  Google Scholar 

  30. Blondel, V.D., Guillaume, J.-L., Lambiotte, R., Lefebvre, E.: Fast unfolding of communities in large networks. J. Stat. Mech. Theor. Exp. 2008(10), P10008 (2008)

    Article  MATH  Google Scholar 

  31. Chen, M., Szymanski, B.K.: Fuzzy overlapping community quality metrics. Soc. Netw. Anal. Min. 5(1), 1–14 (2015). https://doi.org/10.1007/s13278-015-0279-8

    Article  Google Scholar 

  32. Magelinski, T., Bartulovic, M., Carley, K.M.: Measuring node contribution to community structure with modularity vitality. IEEE Trans. Netw. Sci. Eng. 8(1), 707–723 (2021)

    Article  MathSciNet  Google Scholar 

  33. Newman, M.E.J.: Analysis of weighted networks. Phys. Rev. E 70(5), 056131 (2004)

    Article  Google Scholar 

  34. Fortunato, S., Barthelemy, M.: Resolution limit in community detection. Proc. Nat. Acad. Sci. 104(1), 36–41 (2007)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Stephany Rajeh .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2022 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Rajeh, S., Savonnet, M., Leclercq, E., Cherifi, H. (2022). Modularity-Based Backbone Extraction in Weighted Complex Networks. In: Ribeiro, P., Silva, F., Mendes, J.F., Laureano, R. (eds) Network Science. NetSci-X 2022. Lecture Notes in Computer Science(), vol 13197. Springer, Cham. https://doi.org/10.1007/978-3-030-97240-0_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-97240-0_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-97239-4

  • Online ISBN: 978-3-030-97240-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics