Cascade Control and Defense in Complex Networks

Complex networks with a heterogeneous distribution of loads may undergo a global cascade of overload failures when highly loaded nodes or edges are removed due to attacks or failures. Since a small attack or failure has the potential to trigger a global cascade, a fundamental question regards the possible strategies of defense to prevent the cascade from propagating through the entire network. Here we introduce and investigate a costless strategy of defense based on a selective further removal of nodes and edges, right after the initial attack or failure. This intentional removal of network elements is shown to drastically reduce the size of the cascade.

Figure 1

(a) Ratio $G$ as a function of the tolerance parameter $\lambda$. Stars correspond to attacks without defense, while open circles, squares, triangles, and diamonds correspond to the IR of nodes according to the strategies of defense (1)–(4), respectively. (b) Ratio $G$ as a function of the fraction $f$ of nodes intentionally removed according to each of the strategies (1)–(4), for $\lambda =1.5$. Solid circles in (a) correspond to the IR of edges for $\xi =2\lambda$. Each curve corresponds to an average over 20 independent realizations of the network for $\gamma =3.0$, ${\kappa }_0=2$, $N=5000$, and $p=0.001$.