I know there are several proofs for sufficent conditions for a giant component, but can't find them offhand. They'd be useful to put here (actually what I came looking for!) Meekohi 20:46, 4 August 2005 (UTC)
In the theory of random graphs, a giant component is one that contains a positive proportion of the vertices. Here we assume that the number of vertices n is going to infinity. The proportion is independent of n and need not exceed 1/2.