Colorful triangle counting and a MapReduce implementation

Abstract. In this note we introduce a new randomized algorithm for counting triangles in graphs. We show that under mild conditions, the estimate of our algorithm is strongly concentrated around the true number of triangles. Specifi-cally, if p ≥ max ( ∆ lognt, logn√t), where n, t, ∆ denote the number of vertices in G, the number of triangles in G, the maximum number of triangles an edge of G is contained, then for any constant > 0 our unbiased estimate T is concentrated around its expectation, i.e., Pr [|T − E [T] | ≥ E [T]] = o(1). Finally, we present a MapReduce implementation of our algorithm. 1