Depending on the nature of a network, robustness can be a defensive strategy, or an attacking one.

Take an electrical grid, an attack tries to disconnect it, defense means holding it together. On the other hand, with a disease spreading through a social graph, roles flip.

The two paradigms actually share the same math: on a network, an epidemic sustains itself only once β/δ exceeds 1/λ₁, where β is the infection rate, δ is the recovery rate, and λ₁ is the largest eigenvalue of the adjacency matrix.

Drag the slider to vary the edge-removal probability p — the "decoupling" side of the duality: the same fragmenting lattice is also what an epidemic needs to stay contained.

A network that is hard to break is also easier to infect.