Barabási-Albert networks have degree distribution P(k) ~ k^{−γ}. They are remarkably robust to random failures but fragile to targeted removal of high-degree hubs — the "Achilles heel" of scale-free topology.
Left: Barabási-Albert scale-free network. Node size ∝ degree (hubs are large). Removed nodes shown as ×. Right: giant component size vs fraction removed. Random failures (blue) barely affect connectivity — scale-free networks tolerate up to 80% random removal. Targeted hub attack (red) shatters the network quickly, with threshold around 10-15%. The asymmetry is Achilles' heel.