Abstract
The diameter of an unweighted graph is the maximum pairwise distance among its connected vertices. It is one of the main measures in real-world graphs and complex networks. The double sweep is a simple method to find a lower bound for the diameter. It chooses a random vertex and performs two breadth-first searches (BFSes), returning the maximum length among the shortest paths thus found. We propose an algorithm called fringe, which uses few BFSes to find a matching upper bound for almost all the graphs in our dataset of 44 real-world graphs. In the few graphs it cannot, we perform an exhaustive search of the diameter using a cluster of machines for a total of 40 cores. In all cases, the diameter is surprisingly equal to the lower bound found after very few executions of the double sweep method. The lesson learned is that the latter can be used to find the diameter of real-world graphs in many more cases than expected, and our fringe algorithm can quickly validate this finding for most of them.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Alegre, I., Fiol, M., Yebra, J.: Some large graphs with given degree and diameter. J. Graph Theory 10, 219–224 (1986)
Boldi, P., Vigna, S.: Webgraph (2001), http://webgraph.dsi.unimi.it/
Boldi, P., Vigna, S.: The WebGraph framework I: Compression techniques. In: Proc. of the 13th International World Wide Web Conference, pp. 595–601 (2004)
Brandes, U., Erlebach, T.: Network Analysis: Methodological Foundations. Springer, Heidelberg (2005)
Complexnetworks Team: Complex networks and real-world graphs (2008), http://complexnetworks.fr/
Corneil, D.G., Dragan, F.E., Habib, M., Paul, C.: Diameter determination on restricted graph families. Discrete Appl. Math. 113(2-3), 143–166 (2001)
Faloutsos, C.: Graph mining: Patterns, generators and tools. In: Combinatorial Pattern Matching, p. 274 (2009)
Handler, G.: Minimax location of a facility in an undirected tree graph. Transportation Science 7(287–293) (1973)
IMDB: The internet movie database (1990), http://www.imdb.com/
Leskovec, J.: Stanford Network Analysis Package (SNAP) Website (2009), http://snap.stanford.edu
Library, S.L.D.: Citeseer Website (1997), http://citeseer.ist.psu.edu/citeseer.html
Magnien, C., Latapy, M., Habib, M.: Fast computation of empirically tight bounds for the diameter of massive graphs. J. Exp. Algorithmics 13 (2009)
Massa, P., Souren, K.: Trustlet Website (2007), http://www.trustlet.org
Mehlhorn, K., Meyer, U.: External-memory breadth-first search with sublinear i/o. In: Proceedings of the 10th Annual European Symposium on Algorithms, pp. 723–735 (2002)
Sommer, C.: Christian sommer’s homepage (2009), http://www.sommer.jp/graphs/
Zwick, U.: Exact and approximate distances in graphs - a survey. In: Meyer auf der Heide, F. (ed.) ESA 2001. LNCS, vol. 2161, pp. 33–48. Springer, Heidelberg (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Crescenzi, P., Grossi, R., Imbrenda, C., Lanzi, L., Marino, A. (2010). Finding the Diameter in Real-World Graphs. In: de Berg, M., Meyer, U. (eds) Algorithms – ESA 2010. ESA 2010. Lecture Notes in Computer Science, vol 6346. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15775-2_26
Download citation
DOI: https://doi.org/10.1007/978-3-642-15775-2_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15774-5
Online ISBN: 978-3-642-15775-2
eBook Packages: Computer ScienceComputer Science (R0)