Network design involves several areas of research. Computer networks, electrical circuits and transportation problems are some examples. In order to deal with the complexity of these problems, approaches using evolutionary algorithms have been proposed for network design problems (NDPs) with relevant results. Nevertheless, the graph encoding is critical for the performance of evolutionary algorithms for NDPs. The node-depth encoding (NDE) has presented relevant results for NDPs involving undirected graphs. In this sense, this article proposes an extension of NDE for NDPs modeled by directed graphs.