Edge-hopping is when you are trying to get back on stage with the ledge, but so is someone else and then you' fight to get back on, right?
Yes and no.
Scenario: Zelda uses D-Smash to knock Marth off Final Destination. It sends Marth at a low angle, and Marth is at a low enough percent to survive the hit and not get KOed off the side blast line.
Marth's coming back. Should Zelda risk getting in Marth's face and attack with an aerial, or should she just grab the ledge when Marth is close enough?
Option 1: She risks it with an aerial. She about to hit with a f-air.....bam. Dolphin Slashed. Not only is Marth back on the edge, but the angle of the Dolphin Slash's attack stage-spikes you. Now you're behind a stock.
Option 2: She plays it safe and waits for Marth to come up. As soon as he's in range to grab the ledge, Zelda suddenly jumps off and clings to the edge. Marth uses Dolphin Slash to get back up, but since Zelda just now got on the ledge, she has invincibility frames for about a second. Since Marth's Dolphin Slash has only one hitbox, Marth is unable to keep the attack out and hit Zelda after the Inv. frames are gone. Marth goes into helpless, and falls to his death. Zelda is now ahead/closed the gap in stocks!
Depending on the character offstage and the character on the stage, edgehogging is the better option instead of meeting them head on off stage. It's better to edgehog people like Captain Falcon, Mario, Fox, and the tether recoveries, but against the likes of Sonic and Meta Knight, who have 4-5 methods of recovering, and ROB and Pit, who can stay in the air just about forever, it's better to try to confront them and edgeguard.