Erdős–Rényi G(n,p) — Giant Component Phase Transition

As edge probability p crosses 1/n, a giant connected component suddenly emerges. Below threshold: many small trees. Above: a giant spanning component containing Θ(n) vertices.

Nodes n

80
Edge prob p

0.0150
n =
p =
⟨k⟩ = np =
Threshold at 1/n =
Edges:
Components:
Giant component: nodes
Fraction giant: