Central nodes are critical in establishing structural connectivity in a complex network. Attacking such nodes can create real havoc in a complex system. We propose attack strategies based on four types of centers, namely betweenness center, degree center, median, and center. We study the vulnerability of synthetic as well as real-world networks in these center-based attacks. These attacks are node-removal attacks which involve identifying the central node set and removing them from the network. We observed that the attacks based on recalculated network information are more efficient than ones based on initial network information. This work shows that the median-based attack, which is a novel strategy proposed in this work, is highly destructive in real as well as synthetic networks.
Real-world networks are mostly weighted networks. Vulnerability analysis of weighted networks is a new area of research. Bellingeri and Cassi, in their new paper @cite_2 (2017), focus on the change in efficiency of attacks due to weights in the networks. Their work suggest that the vulnerability analysis without considering the weighted structure of networks could be at times misleading.
@cite_2
2739963493 1983345514 2003893010 1892403611
Abstract Complex network response to node loss is a central question in different fields of network science because node failure can cause the fragmentation of the network, thus compromising the system functioning. Previous studies considered binary networks where the intensity (weight) of the links is not accounted for, i.e. a link is either present or absent. However, in real-world networks the weights of connections, and thus their importance for network functioning, can be widely different. Here, we analyzed the response of real-world and model networks to node loss accounting for link intensity and the weighted structure of the network. We used both classic binary node properties and network functioning measure, introduced a weighted rank for node importance (node strength), and used a measure for network functioning that accounts for the weight of the links (weighted efficiency). We find that: (i) the efficiency of the attack strategies changed using binary or weighted network functioning measures, both for real-world or model networks; (ii) in some cases, removing nodes according to weighted rank produced the highest damage when functioning was measured by the weighted efficiency; (iii) adopting weighted measure for the network damage changed the efficacy of the attack strategy with respect the binary analyses. Our results show that if the weighted structure of complex networks is not taken into account, this may produce misleading models to forecast the system response to node failure, i.e. consider binary links may not unveil the real damage induced in the system. Last, once weighted measures are introduced, in order to discover the best attack strategy, it is important to analyze the network response to node loss using nodes rank accounting the intensity of the links to the node. The connections in many networks are not merely binary entities, either present or not, but have associated weights that record their strengths relative to one another. Recent studies of networks have, by and large, steered clear of such weighted networks, which are often perceived as being harder to analyze than their unweighted counterparts. Here we point out that weighted networks can in many cases be analyzed using a simple mapping from a weighted network to an unweighted multigraph, allowing us to apply standard techniques for unweighted graphs to weighted ones as well. We give a number of examples of the method, including an algorithm for detecting community structure in weighted networks and a simple proof of the maximum-flow--minimum-cut theorem. Many social, technological, biological and economical systems are best described by weighted networks, whose properties and dynamics depend not only on their structures but also on the connection weights among their nodes. However, most existing research work on complex network models are concentrated on network structures, with connection weights among their nodes being either 1 or 0. In this paper, we propose a new weighted evolving network model. Numerical simulations indicate that this network model yields three power-law distributions for the node degrees, connection weights and node strengths, respectively. Particularly, some other properties of the distributions, such as the droop-head and heavy-tail effects, can also be reflected by this model. We address a fundamental problem that is systematically encountered when modeling real-world complex systems of societ al relevance: the limitedness of the information available. In the case of economic and financial networks, privacy issues severely limit the information that can be accessed and, as a consequence, the possibility of correctly estimating the resilience of these systems to events such as financial shocks, crises and cascade failures. Here we present an innovative method to reconstruct the structure of such partially-accessible systems, based on the knowledge of intrinsic node-specific properties and of the number of connections of only a limited subset of nodes. This information is used to calibrate an inference procedure based on fundamental concepts derived from statistical physics, which allows to generate ensembles of directed weighted networks intended to represent the real system—so that the real network properties can be estimated as their average values within the ensemble. We test the method both on synthetic and empirical networks, focusing on the properties that are commonly used to measure systemic risk. Indeed, the method shows a remarkable robustness with respect to the limitedness of the information available, thus representing a valuable tool for gaining insights on privacy-protected economic and financial systems.