Multiscale vulnerability of complex networks

Boccaletti, Stefano; Buldú, Javier M.; Criado, Regino; Flores, Julio; Latora, Vito; Pello, Javier; Romance, Miguel

doi:10.1063/1.2801687

Cited by 69 publications

(67 citation statements)

References 15 publications

(11 reference statements)

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“…The aim of the present study is to analyze the vulnerability of AARNs to errors (i.e., the random isolation of an airport) and attacks (i.e., isolation of well-connected airports with the aim of causing the maximum damage to the route network). This assessment is performed by two di↵erent approaches: first, using a multi-scale measure of vulnerability (Boccaletti et al, 2007), and second, examining the e↵ect of the disconnection of a fraction f of wellconnected nodes on the size of the overall giant component. This study can shed light on the robustness of real networks not only for the special case of airline alliances but also for networks sharing similar topological properties.…”

Section: Introductionmentioning

confidence: 99%

Robustness of airline alliance route networks

Lordan

Sallán

Simó

et al. 2015

Communications in Nonlinear Science and Numerical Simulation

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The aim of this study is to analyze the robustness of the three major airline alliances' (i.e., Star Alliance, oneworld and SkyTeam) route networks. Firstly, the normalization of a multi-scale measure of vulnerability is proposed in order to perform the analysis in networks with di↵erent sizes, i.e., number of nodes. An alternative node selection criterion is also proposed in order to study robustness and vulnerability of such complex networks, based on network e ciency. And lastly, a new procedure -the inverted adaptive strategy-is presented to sort the nodes in order to anticipate network breakdown. Finally, the robustness of the three alliance networks are analyzed with (1) a normalized multi-scale measure of vulnerability, (2) an adaptive strategy based on four di↵erent criteria and (3) an inverted adaptive strategy based on the e ciency criterion. The results show that Star Alliance has the most resilient route network, followed by SkyTeam and then oneworld. It was also shown that the inverted adaptive strategy based on the e ciency criterion -inverted e ciency-shows a great success in quickly breaking networks similar to that found with betweenness criterion but with even better results.

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Section: Introductionmentioning

confidence: 99%

Robustness of airline alliance route networks

Lordan

Sallán

Simó

et al. 2015

Communications in Nonlinear Science and Numerical Simulation

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show abstract

“…As the number of links decreases, the network becomes increasingly fragile and b 2 > 1. Reducing N l to a great extent leads to an inexpensive, but very fragile structure (b 2 1 [113,114]). Thus, the decrease of the number of links and the increase of the robustness have opposite tendencies.…”

Section: Proposed Objective Functionmentioning

confidence: 99%

“…where b p l is the betweenness centrality of link l. The multi-scale vulnerability b p of a graph G measures the distribution of shortest paths when links are failing (or attacked) [114] and is very useful when comparing the vulnerability of networks because it helps distinguish between non-identical although very similar network topologies [113]. As shown in [114], if we want to distinguish between two networks with graphs G and G * , one first computes…”

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confidence: 99%

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Abstract:In this work, we describe an approach that allows for optimizing the structure of a smart grid (SG) with renewable energy (RE) generation against abnormal conditions (imbalances between generation and consumption, overloads or failures arising from the inherent SG complexity) by combining the complex network (CN) and evolutionary algorithm (EA) concepts. We propose a novel objective function (to be minimized) that combines cost elements, related to the number of electric cables, and several metrics that quantify properties that are beneficial for SGs (energy exchange at the local scale and high robustness and resilience). The optimized SG structure is obtained by applying an EA in which the chromosome that encodes each potential network (or individual) is the upper triangular matrix of its adjacency matrix. This allows for fully tailoring the crossover and mutation operators. We also propose a domain-specific initial population that includes both small-world and random networks, helping the EA converge quickly. The experimental work points out that the proposed method works well and generates the optimum, synthetic, small-world structure that leads to beneficial properties such as improving both the local energy exchange and the robustness. The optimum structure fulfills a balance between moderate cost and robustness against abnormal conditions. Our approach should be considered as an analysis, planning and decision-making tool to gain insight into smart grid structures so that the low level detailed design is carried out by using electrical engineering techniques.

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Fuzzy Evaluation of Network Vulnerability

Zhang

Xia

Wang

et al. 2015

Qual. Reliab. Engng. Int.

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Vulnerability of networks is not only associated with the ability to resist disturbances but also has an impact on stable development of the networks in the long run. In this paper, a new vulnerability evaluation based on fuzzy logics is proposed. To obtain the vulnerability of the networks, fuzzy logic is utilized to model uncertain environment. Therefore, this evaluation can be divided into two steps. One is to use a graph to represent the network and analyze the main properties of the network, including average path length, edge betweenness, degree, and clustering coefficient. The other is to use fuzzy logics according to the main properties. Namely, this step is to calculate deviations, design rule database, and obtain vulnerability. Two examples are given to show the efficiency and practicability of the proposed method at the end. Copyright © 2015 John Wiley & Sons, Ltd.

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Multiscale vulnerability of complex networks

Cited by 69 publications

References 15 publications

Robustness of airline alliance route networks

Robustness of airline alliance route networks

Optimizing the Structure of Distribution Smart Grids with Renewable Generation against Abnormal Conditions: A Complex Networks Approach with Evolutionary Algorithms

Fuzzy Evaluation of Network Vulnerability

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