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 &quot;re-route&quot; 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?
This operation is called vertex elimination. See for example: &quot;Triangulated Graphs and the Elimination Process&quot;, by Rose (1970).
This type of operation is well-studied, among others, in the context of chordal graphs (see Wikipedia entry about perfect elimination orderings). A related problem of finding an optimal ordering for applying this operation is called Minimum Fill-in.