Skip to main content

On Computing the Diameter of Real-World Directed (Weighted) Graphs

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7276))

Abstract

In this paper we propose a new algorithm for computing the diameter of directed unweighted graphs. Even though, in the worst case, this algorithm has complexity O(nm), where n is the number of nodes and m is the number of edges of the graph, we experimentally show that in practice our method works in O(m) time. Moreover, we show how to extend our algorithm to the case of directed weighted graphs and, even in this case, we present some preliminary very positive experimental results.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Backstrom, L., Boldi, P., Rosa, M., Ugander, J., Vigna, S.: Four Degrees of Separation (2011) arXiv:1111.4570v1

    Google Scholar 

  2. Bansal, S., Khandelwal, S., Meyers, L.: Exploring biological network structure with clustered random networks. BMC Bioinformatics 10(1), 405+ (2009)

    Google Scholar 

  3. Boldi, P., Vigna, S.: The WebGraph Framework I: Compression Techniques. In: Proceedings of the 13th International World Wide Web Conference, pp. 595–601. ACM Press, Manhattan (2003)

    Google Scholar 

  4. Boldi, P., Rosa, M., Vigna, S.: Hyperanf: approximating the neighbourhood function of very large graphs on a budget. In: WWW, pp. 625–634 (2011)

    Google Scholar 

  5. Brandes, U., Erlebach, T.: Network Analysis: Methodological Foundations. Springer (2005)

    Google Scholar 

  6. Broder, A.Z., Kumar, R., Maghoul, F., Raghavan, P., Rajagopalan, S., Stata, R., Tomkins, A., Wiener, J.L.: Graph structure in the web. Computer Networks 33(1-6), 309–320 (2000)

    Article  Google Scholar 

  7. 9th DIMACS Implementation Challenge - Shortest Paths (2006), http://www.dis.uniroma1.it/~challenge9/

  8. Chepoi, V., Dragan, F., Estellon, B., Habib, M., Vaxès, Y.: Diameters, centers, and approximating trees of delta-hyperbolic geodesic spaces and graphs. In: Proceedings of the 24th Annual Symposium on Computational Geometry, SCG 2008, pp. 59–68. ACM, New York (2008)

    Chapter  Google Scholar 

  9. Crescenzi, P., Grossi, R., Habib, M., Lanzi, L., Marino, A.: On Computing the Diameter of Real-World Undirected Graphs. Presented at Workshop on Graph Algorithms and Applications (Zurich–July 3, 2011) and selected for submission to the special issue of Theoretical Computer Science in honor of Giorgio Ausiello in the occasion of his 70th birthday (2011)

    Google Scholar 

  10. Crescenzi, P., Grossi, R., Imbrenda, C., Lanzi, L., Marino, A.: Finding the Diameter in Real-World Graphs. In: de Berg, M., Meyer, U. (eds.) ESA 2010, Part I. LNCS, vol. 6346, pp. 302–313. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  11. Dijkstra, E.: A note on two problems in connexion with graphs. Numerische Mathematik 1, 269–271 (1959)

    Article  MathSciNet  MATH  Google Scholar 

  12. Havlin, S., Cohen, R.: Complex Networks: Structure, Robustness and Function. Cambridge University Press, Cambridge (2010)

    MATH  Google Scholar 

  13. Junker, B.O.H., Schreiber, F.: Analysis of Biological Networks. Wiley Series in Bioinformatics. Wiley Interscience (2008)

    Google Scholar 

  14. Kang, U., Tsourakakis, C.E., Appel, A.P., Faloutsos, C., Leskovec, J.: Hadi: Mining radii of large graphs. TKDD 5(2), 8 (2011)

    Article  Google Scholar 

  15. Kang, U., Tsourakakis, C.E., Faloutsos, C.: PEGASUS: A Peta-Scale graph mining system implementation and observations. In: 2009 Ninth IEEE International Conference on Data Mining, pp. 229–238. IEEE (December 2009)

    Google Scholar 

  16. Latapy, M., Magnien, C.: Measuring Fundamental Properties of Real-World Complex Networks. CoRR abs/cs/0609115 (2006)

    Google Scholar 

  17. Leskovec, J., Faloutsos, C.: Sampling from large graphs. In: Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2006, pp. 631–636. ACM, New York (2006)

    Chapter  Google Scholar 

  18. Leskovec, J., Lang, K.J., Dasgupta, A., Mahoney, M.W.: Community structure in large networks: Natural cluster sizes and the absence of large well-defined clusters. Internet Mathematics 6(1), 29–123 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  19. Mehlhorn, K., Meyer, U.: External-Memory Breadth-First Search with Sublinear I/O. In: Möhring, R.H., Raman, R. (eds.) ESA 2002. LNCS, vol. 2461, pp. 723–735. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  20. Mislove, A., Marcon, M., Gummadi, K.P., Druschel, P., Bhattacharjee, B.: Measurement and analysis of online social networks. In: Proceedings of the 7th ACM SIGCOMM Conference on Internet Measurement, IMC 2007, pp. 29–42. ACM, New York (2007)

    Chapter  Google Scholar 

  21. Newman, M.E.J.: The structure and function of complex networks. SIAM Review 45, 167–256 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  22. Palmer, C.R., Gibbons, P.B., Faloutsos, C.: ANF: a Fast and Scalable Tool for Data Mining in Massive Graphs. In: Proceedings of the 8th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 81–90 (2002)

    Google Scholar 

  23. SNAP: Stanford Network Analysis Package (SNAP) (2009), http://snap.stanford.edu

  24. Takes, F.W., Kosters, W.A.: Determining the diameter of small world networks. In: CIKM, pp. 1191–1196 (2011)

    Google Scholar 

  25. Network datasets (2009), http://toreopsahl.com/datasets/

  26. Wang, F., Moreno, Y., Sun, Y.: Structure of peer-to-peer social networks. Phys. Rev. E 73, 036123 (2006)

    Google Scholar 

  27. WebGraph: WebGraph (2001), http://webgraph.dsi.unimi.it/

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Crescenzi, P., Grossi, R., Lanzi, L., Marino, A. (2012). On Computing the Diameter of Real-World Directed (Weighted) Graphs. In: Klasing, R. (eds) Experimental Algorithms. SEA 2012. Lecture Notes in Computer Science, vol 7276. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30850-5_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-30850-5_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30849-9

  • Online ISBN: 978-3-642-30850-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics