Percolation on Erdős-Rényi and scale-free networks. Compare random failure (robust) vs targeted high-degree attack (fragile) and watch the giant component collapse.
Network type
N nodes150
Mean degree <k>4.0
Fraction removed0.00
Attack strategy
Giant component: —
Moloy-Reed criterion: A giant component exists iff ⟨k²⟩/⟨k⟩ > 2. Scale-free networks (P(k) ~ k−γ, 2<γ<3): ⟨k²⟩ diverges → pc = 0 for random failure, but targeted attack is catastrophic. ER networks: sharp transition at pc = 1/⟨k⟩; both strategies similar.