Skip to main content
SpringerLink
Log in

Fast Approximated Betweenness Centrality of Directed and Weighted Graphs

  • Conference paper
  • First Online:
Complex Networks and Their Applications VII (COMPLEX NETWORKS 2018)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 812))

Included in the following conference series:

Abstract

Node betweenness centrality is a reference metric to identify the most critical spots of a network. However, its exact computation exhibits already high (time) complexity on unweighted, undirected graphs. In some domains such as transportation, weighted and directed graphs can provide more realistic modeling, but at the cost of an additional computation burden that limits the adoption of betweenness centrality for real-time monitoring of large networks. As largely demonstrated in previous work, approximated approaches represent a viable solution for continuous monitoring of the most critical nodes of large networks, when the knowledge of the exact values is not necessary for all the nodes.

This paper presents a fast algorithm for approximated computation of betweenness centrality for weighted and directed graphs. It is a substantial extension of our previous work which focused only on unweighted and undirected networks. Similarly to that, it is based on the identification of pivot nodes that equally contribute to betweenness centrality values of the other nodes of the network. The pivots are discovered via a cluster-based approach that permits to identify the nodes that have the same properties with reference to clusters’ border nodes. The results prove that our algorithm exhibits significantly lower execution time and a bounded and tolerable approximation with respect to state-of-the-art approaches for exact computation when applied to very large, weighted and directed graphs.

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 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 219.99
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.

    The implementation leverages a Scala parallel solution partially based on the Distributed Graph Analytics (DGA) by Sotera: https://github.com/Sotera/distributed-graph-analytics.

  2. 2.

    The adoption of Dijkstra algorithm instead of breadth first search represents a main variant of our FastBC algorithm proposed in this paper.

  3. 3.

    KNR-interpolation is based on K-nearest-neighbor regression [1], a non-parametric supervised machine-learning technique. Each edge is modeled as a data point with multiple topological features. The median speed at time slot t, available for some edges (labeled instances) and missing for other ones (unlabeled instances), represents the target interpolated feature.

References

  1. Altman, N.S.: An introduction to Kernel and nearest-neighbor nonparametric regression. Am. Stat. 46(3), 175–185 (1992)

    Google Scholar 

  2. Altshuler, Y., Puzis, R., Elovici, Y., Bekhor, S., Pentland, A.S.: Augmented betweenness centrality for mobility prediction in transportation networks. In: International Workshop on Finding Patterns of Human Behaviors in Network and Mobility Data (NEMO) (2011)

    Google Scholar 

  3. Bader, D.A., Kintali, S., Madduri, K., Mihail, M.: Approximating betweenness centrality. In: Proceedings of the 5th International Conference on Algorithms and Models for the Web-Graph, WAW 2007, pp. 124–137. Springer, Berlin (2007)

    Google Scholar 

  4. Bader, D.A., Madduri, K.: Parallel algorithms for evaluating centrality indices in real-world networks. In: International Conference on Parallel Processing, 2006. ICPP 2006, pp. 539–550. IEEE (2006)

    Google Scholar 

  5. Bergamini, E., Meyerhenke, H.: Approximating betweenness centrality in fully dynamic networks. Internet Math. 12(5), 281–314 (2016)

    Google Scholar 

  6. Bergamini, E., Meyerhenke, H., Staudt, C.L.: Approximating betweenness centrality in large evolving networks. In: 17th Workshop on Algorithm Engineering and Experiments, ALENEX 2015, pp. 133–146. SIAM, Philadelphia (2015)

    Google Scholar 

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

    Google Scholar 

  8. Borassi, M., Natale, E.: KADABRA is an adaptive algorithm for betweenness via random approximation. In: ESA, LIPIcs, vol. 57, pp. 20:1–20:18. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2016)

    Google Scholar 

  9. Brandes, U.: A faster algorithm for betweenness centrality. J. Math. Sociol. 25(2), 163–177 (2001)

    Google Scholar 

  10. Brandes, U., Pich, C.: Centrality estimation in large networks. Int. J. Bifurc. Chaos 17(07), 2303–2318 (2007)

    Google Scholar 

  11. Chehreghani, M.H., Bifet, A., Abdessalem, T.: Efficient exact and approximate algorithms for computing betweenness centrality in directed graphs. In: Pacific-Asia Conference on Knowledge Discovery and Data Mining. Springer, Cham, pp. 752–764 (2018)

    Google Scholar 

  12. Dugué, N., Perez, A.: Directed Louvain: maximizing modularity in directed networks. Ph.D. thesis, Université d’Orléans (2015)

    Google Scholar 

  13. Freeman, L.C.: Centrality in social networks conceptual clarification. Soc. Netw. 1(3), 215–239 (1978)

    Google Scholar 

  14. Freeman, L.C.: A set of measures of centrality based on betweenness. Sociometry 25, 35–41 (1997)

    Google Scholar 

  15. Furno, A., El Faouzi, N.E., Sharma, R., Zimeo, E.: Reducing pivots of approximated betweenness computation by hierarchically clustering complex networks. In: International Conference on Complex Networks and Their Applications, pp. 65–77. Springer (2017)

    Google Scholar 

  16. Furno, A., El Faouzi, N.E., Sharma, R., Zimeo, E.: Two-level clustering fast betweenness centrality computation for requirement-driven approximation. In: 2017 IEEE International Conference on Big Data (Big Data), pp. 1289–1294. IEEE (2017)

    Google Scholar 

  17. Furno, A., El Faouzi, N.E., Sharma, R., Cammarota, V., Zimeo, E.: A graph-based framework for real-time vulnerability assessment of road networks. In: 2018 IEEE International Conference on Smart Computing (SMARTCOMP), pp. 234–241. IEEE (2018)

    Google Scholar 

  18. Geisberger, R., Sanders, P., Schultes, D.: Better approximation of betweenness centrality. In: Proceedings of the Meeting on Algorithm Engineering and Experiments, pp. 90–100. Society for Industrial and Applied Mathematics (2008)

    Google Scholar 

  19. Hayashi, T., Akiba, T., Yoshida, Y.: Fully dynamic betweenness centrality maintenance on massive networks. Proc. VLDB Endow. 9(2), 48–59 (2015)

    Google Scholar 

  20. Kourtellis, N., Morales, G.D.F., Bonchi, F.: Scalable online betweenness centrality in evolving graphs. In: 2016 IEEE 32nd International Conference on Data Engineering (ICDE), pp. 1580–1581 (2016)

    Google Scholar 

  21. Lee, M.J., Lee, J., Park, J.Y., Choi, R.H., Chung, C.W.: Qube: a quick algorithm for updating betweenness centrality. In: Proceedings of the 21st International Conference on World Wide Web, WWW 2012, pp. 351–360. ACM, New York (2012)

    Google Scholar 

  22. Leicht, E.A., Newman, M.E.J.: Community structure in directed networks. Phys. Rev. Lett. 100(11), 118703 (2008)

    Google Scholar 

  23. Madduri, K., Ediger, D., Jiang, K., Bader, D.A., Chavarria-Miranda, D.: A faster parallel algorithm and efficient multithreaded implementations for evaluating betweenness centrality on massive datasets. In: 2009 IEEE International Symposium on Parallel and Distributed Processing, pp. 1–8. IEEE (2009)

    Google Scholar 

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

    Google Scholar 

  25. Newman, M.E.J., Girvan, M.: Finding and evaluating community structure in networks. Phys. Rev. E 69, 026113 (2004)

    Google Scholar 

  26. Newman, M.J.: A measure of betweenness centrality based on random walks. Soc. Netw. 27(1), 39–54 (2005)

    Google Scholar 

  27. Ohara, K., Saito, K., Kimura, M., Motoda, H.: Accelerating computation of distance based centrality measures for spatial networks. In: International Conference on Discovery Science. Springer, Cham (2016)

    Google Scholar 

  28. Riondato, M., Kornaropoulos, E.M.: Fast approximation of betweenness centrality through sampling. Data Min. Knowl. Discov. 30(2), 438–475 (2016)

    Google Scholar 

  29. Sotera: dga-graphx: Graphx algorithms. https://github.com/Sotera/spark-distributed-louvain-modularity. Accessed Oct 2018

  30. Suppa, P., Zimeo, E.: A clustered approach for fast computation of betweenness centrality in social networks. In: 2015 IEEE International Congress on Big Data, pp. 47–54 (2015)

    Google Scholar 

  31. White, D.R., Borgatti, S.P.: Betweenness centrality measures for directed graphs. Soc. Netw. 16(4), 335–346 (1994)

    Google Scholar 

  32. White, S., Smyth, P.: Algorithms for estimating relative importance in networks. In: Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 266–275. ACM (2003)

    Google Scholar 

Download references

Acknowledgment

This work has been supported by the French research project PROMENADE (grant number ANR-18-CE22-0008), the H2020 framework project SoBigData, grant number 654024, and the GAUSS project (MIUR, PRIN 2015, Contract 2015KWREMX).

Author information

Authors and Affiliations

  1. University of Lyon, IFSTTAR, ENTPE, LICIT UMR_T9401, Lyon, France

    Angelo Furno & Nour-Eddin El Faouzi

  2. University of Tartu, Tartu, Estonia

    Rajesh Sharma

  3. University of Sannio, Benevento, Italy

    Eugenio Zimeo

Authors
  1. Angelo Furno
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nour-Eddin El Faouzi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rajesh Sharma
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Eugenio Zimeo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Angelo Furno .

Editor information

Editors and Affiliations

  1. Nokia Bell Labs, Cambridge, UK

    Luca Maria Aiello

  2. IUT Lumière, University of Lyon, Bron Cedex, France

    Chantal Cherifi

  3. LE2I UMR CNRS 6306 9, University of Burgundy, Dijon Cedex, France

    Hocine Cherifi

  4. Mathematical Institute, University of Oxford, Oxford, UK

    Renaud Lambiotte

  5. Department of Computer Science and Technology, The Computer Laboratory, University of Cambridge, Cambridge, UK

    Pietro Lió

  6. Center for Complex Networks and Systems Research, School of Informatics, Computing, and Engineering, Indiana University, Bloomington, IN, USA

    Luis M. Rocha

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Furno, A., El Faouzi, NE., Sharma, R., Zimeo, E. (2019). Fast Approximated Betweenness Centrality of Directed and Weighted Graphs. In: Aiello, L., Cherifi, C., Cherifi, H., Lambiotte, R., Lió, P., Rocha, L. (eds) Complex Networks and Their Applications VII. COMPLEX NETWORKS 2018. Studies in Computational Intelligence, vol 812. Springer, Cham. https://doi.org/10.1007/978-3-030-05411-3_5

Download citation

Publish with us

Policies and ethics

Search

Navigation