# Standard Name for a vertex removal like operation

I have an operation that looks a lot like vertex removal, and I'm wondering if there's a standard name for it. Given a graph $$G$$ we remove a vertex $$v$$, but instead of removing the edges that were incident on $$v$$, we "re-route" them by connecting all incoming and outgoing edge pairs. Specifically, if $$-$$ is normal vertex deletion and we're trying to define $$\ominus$$, then

$$G \ominus v \equiv G - v + \{ uw | uv \in G \land vw \in G\}.$$

Is there any standard name for this operation?