In Brawl, edge-hogging prevents tether recoveries from grabbing on to ledges.
Mewtwo quickly edge-hogging in Melee by running off the stage and using Teleport in the opposite direction to grab the edge.
Edge-hogging is a tactic in the first three games of the Super Smash Bros. series, where a character holds onto a ledge so that a recovering opponent cannot grab it, taking advantage of the fact that only one character may generally hold onto a ledge at a time. It is a specific type of edge-guarding in that it is a form of recovery disruption.
In Super Smash Bros.
In the original Super Smash Bros., Fox and Ness can use the turn animation out of a dash to change the direction they are facing off of the edge and thus quickly grab it, preparing an edge-hog. This technique is quicker and easier to time with Fox.
In Super Smash Bros. Melee
The most common method of edge-hogging in Melee'ss competitive play is to wavedash back while near the edge, which should result with the characters sliding off of the stage, falling a short distance, and then quickly grabbing the edge. The character then usually uses the invincibility from the edge to avoid being hit by the opponent's recovery move. Other methods include moonwalking, doing a reverse neutral special then sliding off, using certain attacks which allow one to grab the edge faster or while attacking (i.e. Bowser's Whirling Fortress), or simply short hopping back and grabbing the edge. Another method, called the pivot edge-hog, involves pivoting very close to the ledge. The character will skid short distance during the turn-around animation and land on the ledge.
During the edge-hog, smashers typically roll from the ledge as it grants them invulnerability to the recovering opponent's attacks (usually up special) while still retaining possession of the ledge, in addition to usually lasting the longest of all actions and so hogging the edge for longer.
Edge-hogging in Melee earns the "Edge Hog" bonus. The bonus is earned whenever one character is holding an edge and someone else moves into a spot where they can otherwise grab it, regardless of whether the edgehogged character is KO'd.
In Super Smash Bros. Brawl
While it is easier to grab ledges in Brawl, successful edge-hogging requires better timing because the player can no longer edge-hog their opponent by rolling to the stage from the ledge. As a result, some players use hugging to edge-hog their opponents when they aim their recovery move to the ledge. However, edge hogging should be done with precise timing and caution, because if one mistimes the edge hog, the invincibility will wear off and the edge hogger can be attacked, most likely by a deadly stage spike.
In Super Smash Bros. for Nintendo 3DS and Wii U
The entire edge-hogging maneuver has been removed in Super Smash Bros. for Nintendo 3DS and Wii U. Any character can steal the edge from the ledge-grabbing character, causing the previous ledge-grabber to be gently pushed away. This new technique is known as "ledge trumping". The maneuver pushes the previous ledge occupant off of the edge at such an angle that it can easily be followed up with an aerial attack to further deter them from the edge, preventing them from recovering. This makes edge trumping an effective and new technique in the competitive meta-game.
Also new in Smash 4 is the ability for two characters to occupy a ledge, though this is only possible if one of them has a tether recovery. This also leads to a technique called 'tether trumping' which involves performing a ledge-trump using the tether recovery by hanging off the edge until the opponent recovers and grabs the edge and then quickly zipping up the tether and to the edge, trumping the opponent and then quickly deterring them from the edge with an aerial attack.