Erdős–Rényi random graph: a giant connected component emerges discontinuously at ⟨k⟩ = 1
Erdős–Rényi G(n,p): edge probability p = ⟨k⟩/(n−1). At ⟨k⟩ = 1 (p_c = 1/n), the largest component jumps from O(log n) to O(n) — a second-order phase transition with critical exponent β = 1.