Colorful Triangle Counting and a MapReduce Implementation

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. Specifically, if p ≥ max ( log n t , log n √ 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.