Homeomorphism ???

First, we need to note that there are two rather similar terms that can both be used in graph theory, and both denote a type of mapping, i.e. homeomorphism, and homomorphism.

Interestingly, if we analyse these terms only from the ethymological perspective, they mean the same:

homo and homeo are both derived from the Greek word for "same"
morphism is related to the word for "shape, form".

Both of these terms therefore refer to a mapping that in some sense preserves the form.