edge up vs near

edge up is not an adjective while near is an adjective.

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

As verbs, near is a hypernym of edge up; that is, near is a word with a broader meaning than edge up:

Other hypernyms of edge up include approach, come near, come on, draw close, draw near, go up.

edge up (adjective)	near (adjective)
	not far distant in time or space or degree or circumstances
	closely resembling the genuine article
	with or in a close or intimate relationship
	being on the left side
	giving or spending with reluctance
	very close in resemblance

edge up (verb)	near (verb)
push one's way into (a space)	move towards

edge up (adverb)	near (adverb)
	near in time or place or relationship
	(of actions or states) slightly short of or not quite accomplished; all but