Enhancing network robustness against malicious attacks

Abstract

In a recent work [Schneider et al., Proc. Natl. Acad. Sci. USA 108, 3838 (2011)], the authors proposed a simple measure for network robustness under malicious attacks on nodes. Using a greedy algorithm, they found that the optimal structure with respect to this quantity is an onion structure in which high-degree nodes form a core surrounded by rings of nodes with decreasing degree. However, in real networks the failure can also occur in links such as dysfunctional power cables and blocked airlines. Accordingly, complementary to the node-robustness measurement (R(n)), we propose a link-robustness index (R(l)). We show that solely enhancing R(n) cannot guarantee the improvement of R(l). Moreover, the structure of an R(l)-optimized network is found to be entirely different from that of an onion network. In order to design robust networks that are resistant to a more realistic attack condition, we propose a hybrid greedy algorithm that takes both the R(n) and R(l) into account. We validate the robustness of our generated networks against malicious attacks mixed with both nodes and links failure. Finally, some economical constraints for swapping the links in real networks are considered, and significant improvement in both aspects of robustness is still achieved.

Synchrony-optimized networks of Kuramoto oscillators with inertia

“…Our analyses show that the behavior of optimal networks with respect to edge removal is much similar to the non-optimal case, for the three edge removals rules considered. In order to increase the robustness for edge removal, it is possible also to include in the optimization process a measure of robustness, as the ones proposed in [25] and [35], for instance. It is straightforward to change the algorithm in such a way that an edge swap is accepted only if it increases both the synchronization order parameter and the adopted robustness measure.…”

“…We have also studied the robustness of the networks against edge removal. The size of the giant component S (m) is a common topological measure employed in the analysis of how connected a network remains after removing m edges [35]. We have considered three different edge removals rules: random removal; the socalled degree product rule, where one removes first the edges with the highest product of the degrees of the vertices connected to them; and the so-called edgebetweenness rule, where the edges with highest edge-betweenness are removed firstly.…”

“…No appreciable differences in the mean shortest path length l and the clustering coefficient C were observed for the optimal and non-optimal networks. We have also considered the robustness of the networks for edge removal by examining the giant component S (m) [35] against the same three edge removals rules considered in the previous section. Our conclusion is the same: our optimization procedure does not weaken the robustness of the original network against edge removals.…”

Iterative resource allocation for ranking spreaders in complex networks

“…It would be very interesting to test the modified centrality in other dynamic process. For example, one can investigate whether the malicious attack according to the IRA-based degree will cause more harmful results to the giant component of networks [42,43]. In addition, the interdependent networks have attracted much attention recently [44]; how to design an iterative resource allocation in these systems can also be an interesting and important open problem.…”

Immunization and Targeted Destruction of Networks using Explosive Percolation

“…Vaccination of hosts (network nodes) is often the most effective way to prevent large epidemics. Other strategies include manipulating the network topology [2][3][4] or introducing heterogeneity in transmission of the infection [5][6][7].…”