Edge hopping is a technique used to return on-stage from the ledge. It entails dropping from the ledge (by pressing either "back" or "down" on the control stick) and immediately double-jumping. Often, players follow up the double-jump with an air dodge or attack.
Edge hopping is the fastest way to return on-stage from the edge, and is the most flexible - players may perform almost any aerial attack, or air dodge in any direction, directly after edge hopping. However, if the edge hopper is interrupted before landing on-stage, he can be hit off-stage without a second jump, a very unsafe position. Also, characters experience fewer invincibility frames when edge hopping than when rolling or jumping from the ledge.
Ledgehop
Ledgehopping is the act of dropping from the edge of a stage by tapping down or back on the control stick, and immediately using the midair jump to either attack an opponent (recovering or standing on the stage), ledge-stall for invincibility, or wavedash onto the stage, known as a ledgedash.