edge vs periphery

edge and periphery both are nouns.

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

As nouns, periphery is a hyponym of edge; that is, periphery is a word with a more specific, narrower meaning than edge:

edge (noun)	periphery (noun)
a sharp side formed by the intersection of two surfaces of an object	the outside boundary or surface of something
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

edge (verb)	periphery (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