Erdős–Rényi Random Graph Phase Transition
Giant component emergence at ⟨k⟩ = 1 — mean-field percolation in G(n,p)
Parameters
Nodes n =
150
Mean degree ⟨k⟩ =
1.00
Regenerate Graph
Sweep ⟨k⟩ 0→3
Statistics
Edges
0
Components
0
Giant size S
0
S/n (order param)
0.000
p_c = 1/n
—
Giant component fraction
G(n,p): edge prob p = ⟨k⟩/(n−1)
Critical: p_c = 1/n, ⟨k⟩_c = 1
Order param S ≈ 1 − e^{−⟨k⟩S}
(self-consistency, mean-field)