Parallel Triangle Counting and Enumeration Using Matrix Algebra

Triangle counting and enumeration are important kernels that are used to characterize graphs. They are also used to compute important statistics such as clustering coefficients. We provide a simple exact algorithm that is based on operations on sparse adjacency matrices. By parallelizing the individual sparse matrix operations, we achieve a parallel algorithm for triangle counting. The algorithm is generalizable to triangle enumeration by modifying the semiring that underlies the matrix algebra. We present a new primitive, masked matrix multiplication, that can be beneficial especially for the enumeration case. We provide results from an initial implementation for the counting case along with various optimizations for communication reduction and load balance.