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Finding, Counting and Listing All Triangles in Large Graphs, an Experimental Study

  • Thomas Schank
  • Dorothea Wagner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3503)

Abstract

In the past, the fundamental graph problem of triangle counting and listing has been studied intensively from a theoretical point of view. Recently, triangle counting has also become a widely used tool in network analysis. Due to the very large size of networks like the Internet, WWW or social networks, the efficiency of algorithms for triangle counting and listing is an important issue. The main intention of this work is to evaluate the practicability of triangle counting and listing in very large graphs with various degree distributions. We give a surprisingly simple enhancement of a well known algorithm that performs best, and makes triangle listing and counting in huge networks feasible. This paper is a condensed presentation of [SW05].

Keywords

Execution Time Degree Distribution Large Graph High Degree Node Counting Algorithm 
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.

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References

  1. [AYZ97]
    Alon, N., Yuster, R., Zwick, U.: Finding and counting given length cycles. Algorithmica 17(3), 209–223 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  2. [BM01]
    Batagelj, V., Mrvar, A.: A subquadratic triad census algorithm for large sparse networks with small maximum degree. Social Networks 23, 237–243 (2001)CrossRefGoogle Scholar
  3. [FFF99]
    Faloutsos, M., Faloutsos, P., Faloutsos, C.: On power-law relationships of the Internet topology. In: Proceedings of SIGCOMM (1999)Google Scholar
  4. [SW05]
    Schank, T., Wagner, D.: Finding, counting and listing all triangles in large graphs. Technical report, Universität Karlsruhe, Fakultät für Informatik (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Thomas Schank
    • 1
  • Dorothea Wagner
    • 1
  1. 1.University of KalrsruheGermany

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