edge in vs draw close

edge in and draw close both are verbs.

Word	Noun	Adjective	Verb	Adverb
edge in	No	No	Yes	No
draw close	No	No	Yes	No

As verbs, draw close is a hypernym of edge in; that is, draw close is a word with a broader meaning than edge in:

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

edge in (verb)	draw close (verb)
push one's way into (a space)	move or arrange oneself in a comfortable and cozy position
	pull towards oneself
	move towards