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

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].

This work was partially supported by the DFG under grant WA 654/13-2, by the European Commission – Fet Open project COSIN – COevolution and Self-organization In dynamical Networks – IST-2001-33555, and by the EU within the 6th Framework Programme under contract 001907 (integrated project DELIS).