A line digraph of a complete bipartite digraph

In the context of the degree/diameter problem for directed graphs, it is known that the number of vertices of a strongly connected bipartite digraph satisfies a Moore-like bound in terms of its diameter kk and the maximum outdegrees (d1,d2)(d1,d2) of its partite sets of vertices. In this work, we define a family of dense digraphs, the diameter of which is not more than 1, comparable with that of the Moore bipartite digraph of the same order and maximum degree. Furthermore, some of its properties are given, such as the connectivity, spectrum and so on.