Cascade-based attacks on complex networks

We live in a modern world supported by large, complex networks. Examples range from financial markets to communication and transportation systems. In many realistic situations the flow of physical quantities in the network, as characterized by the loads on nodes, is important. We show that for such networks where loads can redistribute among the nodes, intentional attacks can lead to a cascade of overload failures, which can in turn cause the entire or a substantial part of the network to collapse. This is relevant for real-world networks that possess a highly heterogeneous distribution of loads, such as the Internet and power grids. We demonstrate that the heterogeneity of these networks makes them particularly vulnerable to attacks in that a large-scale cascade may be triggered by disabling a single key node. This brings obvious concerns on the security of such systems.Comment: 4 pages, 4 figures, Revte

Dynamic Effects Increasing Network Vulnerability to Cascading Failures

We study cascading failures in networks using a dynamical flow model based on simple conservation and distribution laws to investigate the impact of transient dynamics caused by the rebalancing of loads after an initial network failure (triggering event). It is found that considering the flow dynamics may imply reduced network robustness compared to previous static overload failure models. This is due to the transient oscillations or overshooting in the loads, when the flow dynamics adjusts to the new (remaining) network structure. We obtain {\em upper} and {\em lower} limits to network robustness, and it is shown that {\it two} time scales $\tau$ and $\tau_0$, defined by the network dynamics, are important to consider prior to accurately addressing network robustness or vulnerability. The robustness of networks showing cascading failures is generally determined by a complex interplay between the network topology and flow dynamics, where the ratio $\chi=\tau/\tau_0$ determines the relative role of the two of them.Comment: 4 pages Latex, 4 figure

Cascade control and defense in complex networks

Complex networks with 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.Comment: 4 pages, 2 figures, Revte

The resilience of interdependent transportation networks under targeted attack

Modern world builds on the resilience of interdependent infrastructures characterized as complex networks. Recently, a framework for analysis of interdependent networks has been developed to explain the mechanism of resilience in interdependent networks. Here we extend this interdependent network model by considering flows in the networks and study the system's resilience under different attack strategies. In our model, nodes may fail due to either overload or loss of interdependency. Under the interaction between these two failure mechanisms, it is shown that interdependent scale-free networks show extreme vulnerability. The resilience of interdependent SF networks is found in our simulation much smaller than single SF network or interdependent SF networks without flows.Comment: 5 pages, 4 figure

Network Overload due to Massive Attacks

We study the cascading failure of networks due to overload, using the betweenness centrality of a node as the measure of its load following the Motter and Lai model. We study the fraction of survived nodes at the end of the cascade $p_f$ as function of the strength of the initial attack, measured by the fraction of nodes $p$, which survive the initial attack for different values of tolerance $\alpha$ in random regular and Erd\"os-Renyi graphs. We find the existence of first order phase transition line $p_t(\alpha)$ on a $p-\alpha$ plane, such that if $p <p_t$ the cascade of failures lead to a very small fraction of survived nodes $p_f$ and the giant component of the network disappears, while for $p>p_t$, $p_f$ is large and the giant component of the network is still present. Exactly at $p_t$ the function $p_f(p)$ undergoes a first order discontinuity. We find that the line $p_t(\alpha)$ ends at critical point $(p_c,\alpha_c)$ ,in which the cascading failures are replaced by a second order percolation transition. We analytically find the average betweenness of nodes with different degrees before and after the initial attack, investigate their roles in the cascading failures, and find a lower bound for $p_t(\alpha)$. We also study the difference between a localized and random attacks

Cascade failure analysis of power grid using new load distribution law and node removal rule

The work is supported in part by NSFC (Grant no. 61172070), IRT of Shaanxi Province (2013KCT-04), EPSRC (Grant no.Ep/1032606/1).Peer reviewe

Robustness of scale-free networks to cascading failures induced by fluctuating loads

Taking into account the fact that overload failures in real-world functional networks are usually caused by extreme values of temporally fluctuating loads that exceed the allowable range, we study the robustness of scale-free networks against cascading overload failures induced by fluctuating loads. In our model, loads are described by random walkers moving on a network and a node fails when the number of walkers on the node is beyond the node capacity. Our results obtained by using the generating function method shows that scale-free networks are more robust against cascading overload failures than Erd\H{o}s-R\'enyi random graphs with homogeneous degree distributions. This conclusion is contrary to that predicted by previous works which neglect the effect of fluctuations of loads.Comment: 9 pages, 6 figure