go up vs edge up

go up and edge up both are verbs.

Word	Noun	Adjective	Verb	Adverb
go up	No	No	Yes	No
edge up	No	No	Yes	No

As verbs, edge up is a hyponym of go up; that is, edge up is a word with a more specific, narrower meaning than go up:

Other hyponyms of go up include drive up, bear down on, bear down upon, edge in, close, crowd, push.

go up (verb)	edge up (verb)
increase in value or to a higher point	push one's way into (a space)
burn completely; be consumed or destroyed by fire
move upward
go upward with gradual or continuous progress
be erected, built, or constructed
move towards
travel up