I am trying to understand vertex cut for digraph. I could find this for graphs
Vertex cut is a vertex whose removal increases the number of components in a graph. (D67, Handbook of Graph Theory by Gross)
and components for digraphs defined here. I am interested in st-connectivity so if the digraph definition is analogous with the undirected definition, then the removal of the cut should increase the number of st-connected components. So
What is the definition of vertex-cut for digraph?