Whether as telecommunications or power systems, networks are very important in everyday life. Maintaining these networks properly functional and connected, even under attacks or failures, is of special concern. This topic has been previously studied with a whole network robustness perspective,modeling networks as undirected graphs (such as roads or simply cables). This perspective measures the average behavior of the network after its last node has failed. In this article we propose two alternatives to well-known studies about the robustness of the backbone Internet: to use a supply network model and metrics for its representation (we called it the Go-Index), and to use robustness metrics that can be calculated while disconnections appear. Our research question is: if a smart adversary has a limited number of strikes to attack the Internet, how much will the damage be after each one in terms of network disconnection? Our findings suggest that in order to design robust networks it might be better to have a complete view of the robustness evolution of the network, from both the infrastructure and the users perspective.
The stability of scale-free network under degree-based attacks was studied on @cite_11 . Experimental results are shown in @cite_8 who also consider sequential and simultaneous attacks as well as centrality measure strategies. To get closer to a real world strategy scenario on @cite_3 @cite_26 studied the resilience of scale-free networks to a variety of attacks with different amounts of information available to the attacker about the network.
@cite_8 @cite_26 @cite_3 @cite_11
2327083405 2107538138 1967385589 2131244179
We study the stability of random scale-free networks to degree-dependent attacks. We present analytical and numerical results to compute the critical fraction @math of nodes that need to be removed for destroying the network under this attack for different attack parameters. We study the effect of different defense strategies, based on the addition of a constant number of links on network robustness. We test defense strategies based on adding links to either low degree, middegree or high degree nodes. We find using analytical results and simulations that the middegree nodes defense strategy leads to the largest improvement to the network robustness against degree-based attacks. We also test these defense strategies on an internet autonomous systems map and obtain similar results. In this work, we estimate the resilience of scale-free networks on a number of different attack methods. We study a number of different cases, where we assume that a small amount of knowledge on the network structure is available, or can be approximately estimated. We also present a class of real-life networks that prove to be very resilient on intentional attacks, or equivalently much more difficult to immunize completely than most model scale-free networks. We study the response of complex networks subject to attacks on vertices and edges. Several existing complex network models as well as real-world networks of scientific collaborations and Internet traffic are numerically investigated, and the network performance is quantitatively measured by the average inverse geodesic length and the size of the largest connected subgraph. For each case of attacks on vertices and edges, four different attacking strategies are used: removals by the descending order of the degree and the betweenness centrality, calculated for either the initial network or the current network during the removal procedure. It is found that the removals by the recalculated degrees and betweenness centralities are often more harmful than the attack strategies based on the initial network, suggesting that the network structure changes as important vertices or edges are removed. Furthermore, the correlation between the betweenness centrality and the degree in complex networks is studied. We study the tolerance of a scale-free network (having a connectivity distribution P(k)∼k−γ) under systematic variation of the attack strategy. In an attack, the probability that a given node is destroyed, depends on the number of its links k via W(k)∼kα, where α varies from −∞ (most harmless attack) to +∞ (most harmful “intentional” attack). We show that the critical fraction pc needed to disintegrate the network increases monotonically when α is decreased and study how at pc the topology of the diluted network depends on the attack strategy.