Erdős-Rényi G(n,p)

Nodes n: 80 Avg degree ⟨k⟩ = np: 1.00 Auto-animate p

p (edge prob)—

Edges—

Giant comp. size—

Giant / n—

# components—

2nd largest—

⟨k⟩ measured—

Threshold: p* = 1/n, ⟨k⟩ = 1
Below: largest O(log n)
Above: giant ~ β·n
β solves β = 1 - e^−⟨k⟩β
(self-consistent equation)