Giant component

An Erdős–Rényi–Gilbert random graph with 1000 vertices at the critical edge probability , showing a large component and many small ones. At this edge probability, the large component is not yet a giant component: it contains only a sublinear number of vertices.

In network theory, a giant component is a connected component of a given random graph that contains a significant fraction of the entire graph's vertices.

More precisely, in graphs drawn randomly from a probability distribution over arbitrarily large graphs, a giant component is a connected component whose fraction of the overall number of vertices is bounded away from zero. In sufficiently dense graphs distributed according to the Erdős–Rényi model, a giant component exists with high probability.