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.