Interdependent networks show first-order discontinuous collapse (Buldyrev et al. 2010)
Giant component: — | Cascade rounds: —
Buldyrev et al. (Nature 2010): two interdependent networks A and B where fraction q of nodes in A depend on specific nodes in B (and vice versa). Initial failure of fraction (1-p) of A nodes triggers cascading failures. Unlike single-layer percolation (2nd order), the multiplex shows a 1st-order (discontinuous) transition — the giant component collapses abruptly. Critical p_c is much higher than single-layer. Real-world: power grid + internet interdependence.