What are transitive successor and transitive predecessor in the graph? I'm reading a book on compilers, Engineering a Compiler, 2nd ed. by Keith D. Cooper &amp; Linda Torczon and I came a across two new terms that I can't understand, they are:


  transitive successor and transitive predecessor of a node $i$


I tried to find definitions of those online, but I'm having hard time with it. Everything I find talks about transitive reduction.

Can someone give a clear definition of this? Any help is appreciated.
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.