The eccentric digraph operator takes a graph G (either directed or undirected) as a basis and transforms it into a digraph ED(G) with the same vertices as G and where there is an arc from a vertex u to a vertex v if and only if v is a farthest vertex from u in G, that is, v is an eccentric vertex of u. The eccentric digraph ED(G) induces a partition of the set of all digraphs of given order. In this paper, we deal with some properties of the partition.