# Terminology for operation where vertex is deleted and its parents/children are connected

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.

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I would just say "the successors of $X$ are added as children of the predecessors of $X$, and $X$ is removed." It's a little cumbersome I guess. –  nullUser Aug 15 '12 at 14:26

bipartite or multimodal projection

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Thanks Nate. I had previously considered using the term "vertex contraction" but as you mentioned that does not quite fit the bill. "Smoothing" is close, but as I'm dealing with vertices of degree >2 it would not apply. –  Shawn Chin Aug 15 '12 at 14:49