Erdős-Rényi Percolation — Giant Component Threshold

In an Erdős-Rényi random graph G(n,p), a giant connected component suddenly emerges at the critical threshold p_c = 1/n (average degree ⟨k⟩=1). Below: many small clusters. At threshold: susceptibility peaks. Above: a single component spans O(n) nodes.

N =
p =
⟨k⟩ =
Giant component: nodes (%)
Num components:
Susceptibility χ:

Critical p×N = 1.0