I'm currently documenting an algorithm which involves deleting a node in a directed dependency graph while maintaining the implied dependencies between its parents and children.
Take for example the following graph:
Edges are added from all parents to children before node
X is deleted to ensure that the implied dependencies are maintained.
Question: Is there a standard terminology for such an operation?
Update: Thanks to a change in my algorithm, node
X is now guaranteed to have only one parent. This reduces the above operation to a simple node contraction with the parent. While my immediate problem is now solved, I'm leaving the question open and unanswered as I'm still curios to know the solution had my requirements not changed.