Network Attack & Percolation

Targeted vs random attack — scale-free vs random network robustness

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Network visualization
Giant component size vs f
Network percolation: as nodes are removed, the giant connected component (GCC) shrinks.
Scale-free networks (Barabási-Albert, degree ~ k^{-3}) are robust to random failures (hubs rarely hit) but fragile to targeted attacks (remove hubs first → instant collapse).
Erdős-Rényi random networks are equally vulnerable to both — no hubs to exploit. This is the structural vulnerability of the internet and biological networks.