top, upper
the top edge of the picture frame

bottom, lower
inner, inside
outer, outermost, outside
front, rear
left, right
the left edge of the image

northern, southern, etc.
far, near, opposite
She could see rocky cliffs on the opposite edge of the lake.

bevelled/beveled, curved, raised, rounded, scalloped, smooth, straight
the rounded edges of her collarbone
a mirror with a bevelled/beveled edge

exposed
cut, frayed
Flip the fabric over so the cut edge is now to your left.
My fingers played with the frayed edges of my jeans.

very
Erosion has left the house perched on the very edge of the cliff.

cliff, forest, water's
A row of boats was beached at the water's edge.

reach
We had reached the edge of the map and didn't know which way to go.

skirt
The road skirts the western edge of the forest.

clutch, grab, grasp, grip
I gripped the edge of my desk to steady myself.

catch
My foot caught the edge of the table.

border, line
Trees lined the edges of the path.

define, mark
A trellis provided shade and defined the edges of the courtyard.

form
The building forms the northern edge of the courtyard.

align
sand, seal, trim

along the edge, around the edge, round the edge (esp. BrE)
Smoke was making its way around the edges of the door.

at the edge
Soon we were at the edge of the woods.

on the edge
She sat on the edge of her bed.

over the edge
The car rolled over the edge of the cliff.

right on the edge
They live right on the edge of town.

razor-sharp, sharp
cutting
serrated
a knife with a serrated edge

jagged, ragged, rough
smooth
blunt

sharpen

competitive
slight
big (informal, esp. AmE), decided, decisive, definite
winning
extra
Their training gave them an extra edge.

technological

give sb/sth
gain, have, hold
to gain a competitive edge over rival suppliers

keep, maintain, retain
Taiwan still retained a decisive edge in many industries.

lose

edge over
The intensive training she had done gave her the edge over the other runners.