The Wikipedia page on graph homeomorphism describes an opposite operation of edge subdivision that it calls smoothing.
What is the customary name of this operation in mathematics? Is there a name for the graph obtained by performing "smoothing" repeatedly as many times as possible?
I have seen the term subdivision used in many places, but I have not seen the term smoothing anywhere else than on Wikipedia.
In particular, I am looking for a good name to use in a software package for the following operation: perform smoothing as many times as possible (thus removing all degree-2 vertices). Is smoothen a reasonable name for this operation, that would feel natural to a mathematician?