Triangle counting for scale-free graphs at scale in distributed memory

Abstract

Triangle counting has long been a challenge problem for sparse graphs containing high-degree "hub" vertices that exist in many real-world scenarios. These high-degree vertices create a quadratic number of wedges, or 2-edge paths, which for brute force algorithms require closure checking or wedge checks. Our work-in-progress builds on existing heuristics for pruning the number of wedge checks by ordering based on degree and other simple metrics. Such heuristics can dramatically reduce the number of required wedge checks for exact triangle counting for both real and synthetic scale-free graphs. Our triangle counting algorithm is implemented using HavoqGT, an asynchronous vertex-centric graph analytics framework for distributed memory. We present a brief experimental evaluation on two large real scale-free graphs: a 128B edge web-graph and a 1.4B edge twitter follower graph, and a weak scaling study on synthetic Graph500 RMAT graphs up to 274.9 billion edges.