Fast Parallel Graph Triad Census and Triangle Counting on Shared-memory Platforms

Triad census is a graph analytic used for comparative network analysis and to characterize local structure in directed networks. For large sparse graphs, an algorithm by Batagelj and Mrvar is considered the state-of-the-art for computing triad census. In this paper, we present a new parallel algorithm for triad census. Our algorithm takes advantage of a specific graph vertex identifier ordering to reduce the operation count. We also develop several new variants for exact triangle counting in large sparse, undirected graphs. We show that our parallel triangle counting variants outperform other recently-developed triangle counting methods on current Intel multicore and manycore processors. We also achieve good strong scaling for both triad census and triangle counting on these platforms.