The following problem arises in the design of some interconnection networks for distributed systems. Namely, to construct digraphs with given maximum out-degree, reduced diameter, easy routing, good connectivity, and good expandability. To this end, a new method based on the concept of partial line digraph is presented. This proposal, which turns out to be a generalization of the so-called line digraph technique, allows us to obtain digraphs that satisfy all the above-mentioned requirements. In particular it is shown that the partial line digraphs of Kautz digraphs solve the (d. digraph problem-i.e. to minimize the diameter D in a digraph of maximum outdegree d and number of vertices S-for any in the range Index Terms- Communication network, connectivity maximization, (d. Y) digraph problem, expandability, fault-tolerance, line digraph, routing algorithm. an-l + (P2+ . . . + 1 5 -1- 5 drl + P1.