An oriented graphD is an orientation of a simple graph G, i.e., D is obtained from G by assigning a direction for each edge. Alternatively, an oriented graph is a directed graph with no symmetric pair of arcs. Despite the oriented case being less studied in the literature, compared to the undirected case, some of the oldest papers on graph convexity deal exactly with the oriented case. For the oriented case, two convexities have been studied in the literature: the geodesic and the \(P_3\) .