Flatten directed, acyclic graph

Question

Suppose I have a directed, acyclic graph where $A \to B$ represents that $A$ depends on $B$.

I want to 'flatten' this graph so that each vertex has an edge to all direct and indirect dependencies. Ie. create a new graph such that if $A \to B$ and $B \to C$ in the original graph, then the new graph will contain $A \to B$, $B \to C$, and $A \to C$.

What is the proper name for this operation, and are there existing algorithms that can perform this task?

Answer 1

This is the transitive closure graph (or sometimes reachability graph) and can be implemented in nearly all graph software. In Mathematica:

g = Graph[{1 \[DirectedEdge] 2, 1 \[DirectedEdge] 3, 
   1 \[DirectedEdge] 4, 3 \[DirectedEdge] 4, 2 \[DirectedEdge] 4, 
   4 \[DirectedEdge] 5}, VertexLabels -> "Name"]

TransitiveClosureGraph[g, VertexLabels -> "Name"]