Terminology: customary name of graph "smoothing" 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?

Wikipedia also calls it edge contraction. There is a very similar MSE question 197972 removing degree-2 vertices from a graph.
