A directed graph G= (V,E) consists of a set of vertices V, and a set of edges E such that each

element e in E is an ordered pair (u,v), denoting an edge directed from u to v. In a directed

graph, a directed cycle of length three is a triple of vertices (x,y,z) such that each of (x,y) (y,z)

and (z,x) is an edge in E. Write a Mapreduce algorithm whose input is a directed graph presented as a list of edges (on a file in HDFS), and whose output is the list of all directed cycles of length three in G. Write the pseudocode for the map and reduce methods in each round. Also present an analysis of the total communication cost in each round, as a function of the number of vertices and the number of edges in the graph.