Triangle counting in networks using a multi-level branching technique

Abstract

Counting triangles in networks is a fundamental problem in network science. In addition, because we are forced to manage very large real-world networks, current triangle counting algorithms naturally require a distributed computing system. In this paper, we propose a distributed triangle counting algorithm based on both the vertex-centric and node-iterator models and using the multi-level branching technique. Multi-level branching is a method that constructs an ordered graph structure based on levels. This method not only facilitates an efficient triangle counting process, but also guarantees the computational integrity of each split in the distributed triangle counting process. First, we describe a level-based triangle counting algorithm based on both the vertex-centric model and the node-iterator algorithm. Then, we develop a distributed implementation of the proposed algorithm using GraphChi. The main advantages of the proposed algorithm are that the execution is simple yet effective, and thus its parallelization is efficient. Experiments on real-world networks verify its performance, particularly, its near-linear parallelization scalability.