What are transitive successor and transitive predecessor in the graph?
If you ask Google with "transitive successor" (including the double quotes) you get several book
references, and access to some pages (which I cannot read right now,
because of a local problem). Considering that successor is a
relation between the nodes of the directed graph, "transitive
successor" should naturally be its transitive closure. One book is
apparently using the term "direct successor" to be precise and avoid
confusion with "transitive successor" which could occur when using
"successor" alone.