Combined Heuristic Attack Strategy on Complex Networks

Abstract

Usually, the existence of a complex network is considered an advantage feature and efforts are made to increase its robustness against an attack. However, there exist also harmful and/or malicious networks, from social ones like spreading hoax, corruption, phishing, extremist ideology, and terrorist support up to computer networks spreading computer viruses or DDoS attack software or even biological networks of carriers or transport centers spreading disease among the population. New attack strategy can be therefore used against malicious networks, as well as in a worst-case scenario test for robustness of a useful network. A common measure of robustness of networks is their disintegration level after removal of a fraction of nodes. This robustness can be calculated as a ratio of the number of nodes of the greatest remaining network component against the number of nodes in the original network. Our paper presents a combination of heuristics optimized for an attack on a complex network to achieve its greatest disintegration. Nodes are deleted sequentially based on a heuristic criterion. Efficiency of classical attack approaches is compared to the proposed approach on Barabási-Albert, scale-free with tunable power-law exponent, and Erdős-Rényi models of complex networks and on real-world networks. Our attack strategy results in a faster disintegration, which is counterbalanced by its slightly increased computational demands.

Octahedral–Tetrahedral Systems [Co(dppmO,O)3]2+[CoX4]2– Showing Slow Magnetic Relaxation with Two Relaxation Modes

“…A simultaneous fitting of the susceptibility and magnetization data led to the optimum set of magnetic parameters listed in Table . Nonlinear optimization of magnetic data (both dc and ac) was conducted by the MIF&FIT program that utilizes modern genetic algorithms along with other advanced methods. − The spin Hamiltonian formalism is legitimate to use in the present case of the compressed tetragonal bipyramid for the cationic unit since the daughter ground term is orbitally nondegenerate 4 A 1g .…”

Response of quantum spin networks to attacks

“…Common kinds of attacks are adding or removing nodes or links, where the nodes or links are chosen randomly or preferentially based on the degree or centrality measures of the attacked node. They find that the response of the network depends on the kind of network -complex or random -and how the attacked nodes are chosen -random or preferential [36][37][38][39][40][41]. We briefly study the response of the imprinted networks to classical attacks in Appendix A.…”

A Framework of Hierarchical Attacks to Network Controllability

“…For targeted attacks, it is also assumed that the targeted object is more important than the others in maintaining the network connectedness. Commonly used measures of importance include degree centrality, betweenness centrality, neighborhood similarity [28], branch weighting [29], and structural holes [30]. However, ranking the importance of nodes or edges is practically intractable for large-scale networks, since most measures cannot guarantee that removing the targeted object will definitely cause a greatest effect of damage on the network.…”