In this article we introduce a pseudo-metric on directed graphs, which forms there a family of convex sets. The graphs without d-convex sets, except empty set, sets of one vertex and set of all vertexes, are called d-convex simple. We give an iterative method of description of the set of all directed d-convex simple graphs. Then we research the structure of directed d-convex simple graphs and do this by using some new operations and new graphs. After that we show that the set of directed d-convex simple graphs contains all known undirected d-convex simple graphs.