Approximate Triangle Counting

Triangle counting is an important problem in graph mining. Clustering coefficients of vertices and the transitivity ratio of the graph are two metrics often used in complex network analysis. Furthermore, triangles have been used successfully in several real-world applications. However, exact triangle counting is an expensive computation. In this paper we present the analysis of a practical sampling algorithm for counting triangles in graphs. Our analysis yields optimal values for the sampling rate, thus resulting in tremendous speedups ranging from \emph{2800}x to \emph{70000}x when applied to real-world networks. At the same time the accuracy of the estimation is excellent. Our contributions include experimentation on graphs with several millions of nodes and edges, where we show how practical our proposed method is. Finally, our algorithm's implementation is a part of the \pegasus library (Code and datasets are available at (http://www.cs.cmu.edu/~ctsourak/).) a Peta-Graph Mining library implemented in Hadoop, the open source version of Mapreduce.