periphery vs edge

periphery and edge both are nouns.

Word	Noun	Adjective	Verb	Adverb
periphery	Yes	No	No	No
edge	Yes	No	Yes	No

As nouns, edge is a hypernym of periphery; that is, edge is a word with a broader meaning than periphery:

Other hypernyms of periphery include bound, boundary.

periphery (noun)	edge (noun)
the outside boundary or surface of something	a sharp side formed by the intersection of two surfaces of an object
	the outside limit of an object or area or surface; a place farthest away from the center of something
	a slight competitive advantage
	the attribute of urgency in tone of voice
	the boundary of a surface
	a line determining the limits of an area

periphery (verb)	edge (verb)
	lie adjacent to another or share a boundary
	provide with an edge
	advance slowly, as if by inches
	provide with a border or edge