Cascading Failure — Interdependent Networks

Buldyrev et al. (Nature, 2010) showed that two interdependent networks (e.g., power grid and internet, where each node needs a counterpart in the other to function) are dramatically more fragile than isolated networks. In a single network, a random failure of fraction p causes gradual percolation. In interdependent networks, the cascade is abrupt: failures in A knock out B nodes, which knock out more A nodes, in a catastrophic first-order phase transition. The critical threshold p_c is much higher than for isolated networks — the system appears robust until it suddenly collapses.