Mean-Field Percolation & Giant Component

In random graph percolation, a giant connected component emerges abruptly at p_c = 1/⟨k⟩ (Erdős-Rényi). Below p_c all components are small (O(log N)); above p_c a giant component containing O(N) nodes appears. Mean-field critical exponents: β=1, γ=1, τ=5/2.