Triangle counting in large networks: a review

Abstract

Counting and enumeration of local topological structures, such as triangles, is an important task for analyzing large real‐life networks. For instance, triangle count in a network is used to compute transitivity—an important property for understanding graph evolution over time. Triangles are also used for various other tasks completed for real‐life networks, including community discovery, link prediction, and spam filtering. The task of triangle counting, though simple, has gained wide attention in recent years from the data mining community. This is due to the fact that most of the existing algorithms for counting triangles do not scale well to very large networks with millions (or even billions) of vertices. To circumvent this limitation, researchers proposed triangle counting methods that approximate the count or run on distributed clusters. In this paper, we discuss the existing methods of triangle counting, ranging from sequential to parallel, single‐machine to distributed, exact to approximate, and off‐line to streaming. We also present experimental results of performance comparison among a set of approximate triangle counting methods built under a unified implementation framework. Finally, we conclude with a discussion of future works in this direction.