Remove nodes randomly and find the percolation threshold — scale-free networks have p_c = 0
BA Scale-free (random removal)
ER Random (random removal)
BA Scale-free (targeted)
ER threshold f_c = 1−1/⟨k⟩
Cohen et al. (2000): Scale-free networks (P(k)~k−3, BA model) have p_c → 0 under random node removal — they are extremely robust because hubs are rarely hit. But targeted removal of hubs causes rapid collapse.
Erdős-Rényi networks have threshold f_c = 1 − 1/⟨k⟩ for random removal.
This asymmetry drives internet resilience design and epidemic vaccination strategy.