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.
On @cite_4 was found that targeted attack can be more effective when they are directed to bottlenecks rather than hubs. On @cite_18 authors present partial values of @math -index while nodes are disconnected, showing the importance of a well chosen robustness metric for performing the attacks.
@cite_18 @cite_4
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In this article we present Miuz, a robustness index for complex networks. Miuz measures the impact of disconnecting a node from the network while comparing the sizes of the remaining connected components. Strictly speaking, Miuz for a node is defined as the inverse of the size of the largest connected component divided by the sum of the sizes of the remaining ones. We tested our index in attack strategies where the nodes are disconnected in decreasing order of a specified metric. We considered Miuz and other well-known centrality measures such as betweenness, degree, and harmonic centrality. All of these metrics were compared regarding the behavior of the robustness (R- index) during the attacks. In an attempt to simulate the internet backbone, the attacks were performed in complex networks with power-law degree distributions (scale-free networks). Preliminary results show that attacks based on disconnecting a few number of nodes Miuz are more dangerous (decreasing the robustness) than the same attacks based on other centrality measures. We believe that Miuz, as well as other measures based on the size of the largest connected component, provides a good addition to other robustness metrics for complex networks. 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. Abstract As network analysis methods prevail, more metrics are applied to co-word networks to reveal hot topics in a field. However, few studies have examined the relationships among these metrics. To bridge this gap, this study explores the relationships among different ranking metrics, including one frequency-based and six network-based metrics, in order to understand the impact of network structural features on ranking themes on co-word networks. We collected bibliographic data from three disciplines from Web of Science (WoS), and generated 40 simulation networks following the preferential attachment assumption. Correlation analysis on the empirical and simulated networks shows strong relationships among the metrics. Their relationships are consistent across disciplines. The metrics can be categorized into three groups according to the strength of their correlations, where Degree Centrality, H-index, and Coreness are in one group, Betweenness Centrality, Clustering Coefficient, and frequency in another, and Weighted PageRank by itself. Regression analysis on the simulation networks reveals that network topology properties, such as connectivity, sparsity, and aggregation, influence the relationships among selected metrics. In addition, when comparing the top keywords ranked by the metrics in the three disciplines, we found the metrics exhibit different discriminative capacity. Coreness and H-index may be better suited for categorizing keywords rather than ranking keywords. Findings from this study contribute to a better understanding of the relationships among different metrics and provide guidance for using them effectively in different contexts.