A Framework for Description and Analysis of Sampling-based Approximate Triangle Counting Algorithms

Counting the number of triangles in a large graph has many important applications in network analysis. Several frequently computed metrics such as the clustering coefficient and the transitivity ratio need to count the number of triangles. In this paper, we present a randomized framework for expressing and analyzing approximate triangle counting algorithms. We show that many existing approximate triangle counting algorithms can be described in terms of probability distributions given as parameters to the proposed framework. Then, we show that our proposed framework provides a quantitative measure for the quality of different approximate algorithms. Finally, we perform experiments on real-world networks from different domains and show that there is no unique sampling technique outperforming the others for all networks and the quality of sampling techniques depends on different factors such as the structure of the network, the vertex degree-triangle correlation and the number of samples.