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.
Targeted attacks have been thoroughly studied to analyze network robustness. Holme tested node degree and betweenness centrality strategies using simultaneous and sequential attacks. On @cite_21 simultaneous attacks based on network centrality measures and random attacks were studied.
@cite_21
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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. We examine the robustness of networks under attack when the attacker sequentially selects from a number of different attack strategies, each of which removes one node from the network. Network robustness refers to the ability of a network to maintain functionality under attack, and the problem-dependent context implies a number of robustness measures exist. Thus, we analyze four measures: (1) entropy, (2) efficiency, (3) size of largest network component, and suggest to also utilize (4) pairwise connectivity. Six network centrality measures form the set of strategies at the disposal of the attacker. Our study examines the utility of greedy strategy selection versus random strategy selection for each attack, whereas previous studies focused on greedy selection but limited to only one attack strategy. Using a set of common complex network benchmark networks, in addition to real-world networks, we find that randomly selecting an attack strategy often performs well when the attack strategies are of high quality. We also examine defense against the attacks by adding k edges after each node attack and find that the greedy strategy is most useful in this context. We also observed that a betweenness-based attack often outperforms both random and greedy strategy selection, the latter often becoming trapped in local optima. 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. An analysis is conducted on the robustness of measures of centrality in the face of random error in the network data. We use random networks of varying sizes and densities and subject them (separately) to four kinds of random error in varying amounts. The types of error are edge deletion, node deletion, edge addition, and node addition. The results show that the accuracy of centrality measures declines smoothly and predictably with the amount of error. This suggests that, for random networks and random error, we shall be able to construct confidence intervals around centrality scores. In addition, centrality measures were highly similar in their response to error. Dense networks were the most robust in the face of all kinds of error except edge deletion. For edge deletion, sparse networks were more accurately measured.