Onion-like network topology enhances robustness against malicious attacks

Herrmann, Hans J.; Schneider, Christian; Moreira, André A.; Andrade, José S.; Havlin, Shlomo

doi:10.1088/1742-5468/2011/01/p01027

Cited by 155 publications

(119 citation statements)

References 23 publications

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“…We are interested in the more substantial destruction of the network. Therefore, we use in our paper a measure of network damage , Unique Robustness Measure ( -index) [45,46], defined as…”

Section: Network Their Types Models and Measures Of Robustnessmentioning

confidence: 99%

Combined Heuristic Attack Strategy on Complex Networks

Šimon

Ľuptáková

Huraj

et al. 2017

Mathematical Problems in Engineering

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Usually, the existence of a complex network is considered an advantage feature and efforts are made to increase its robustness against an attack. However, there exist also harmful and/or malicious networks, from social ones like spreading hoax, corruption, phishing, extremist ideology, and terrorist support up to computer networks spreading computer viruses or DDoS attack software or even biological networks of carriers or transport centers spreading disease among the population. New attack strategy can be therefore used against malicious networks, as well as in a worst-case scenario test for robustness of a useful network. A common measure of robustness of networks is their disintegration level after removal of a fraction of nodes. This robustness can be calculated as a ratio of the number of nodes of the greatest remaining network component against the number of nodes in the original network. Our paper presents a combination of heuristics optimized for an attack on a complex network to achieve its greatest disintegration. Nodes are deleted sequentially based on a heuristic criterion. Efficiency of classical attack approaches is compared to the proposed approach on Barabási-Albert, scale-free with tunable power-law exponent, and Erdős-Rényi models of complex networks and on real-world networks. Our attack strategy results in a faster disintegration, which is counterbalanced by its slightly increased computational demands.

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“…We are interested in the more substantial destruction of the network. Therefore, we use in our paper a measure of network damage , Unique Robustness Measure ( -index) [45,46], defined as…”

Section: Network Their Types Models and Measures Of Robustnessmentioning

confidence: 99%

Combined Heuristic Attack Strategy on Complex Networks

Šimon

Ľuptáková

Huraj

et al. 2017

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…The maximum value of the Pearson coefficient, r = 1, is therefore to be realized as a limiting value of r approaching one from below (r → 1−0). In this limit, the structure of the bimodal network consists of two random regular networks connected by a few number of edges, which is known as the onion-like structure [11][12][13] and is always possible even if the degree inhomogeneity is weak. On the other hand, in the construction of networks with negative values of the Pearson coefficient, the total number of edges from nodes of K degree should be equal to the total number of edges from nodes of m degree: KP (K) = mP (m).…”

Section: A Correlation Between the Nearest Neighbor Degreesmentioning

confidence: 99%

“…where S(p) is the node ratio of the giant component to the initial network when the remaining node fraction is p [11,12]. Since S(p) ≤ p, the values of R reside in the range 0 ≤ R ≤ 1/2.…”

Section: Network Robustness In Terms Of the Giant Component Collapsementioning

confidence: 99%

“…Recently Schneider et al through numerical simula-tions and Tanizawa et al with strict analytical arguments found that the most robust network structure with a given degree distribution under both possibilities of random failure of nodes and degree-based targeted attack is a set of hierarchically connected random regular graphs with the ratios of node numbers of each graph in accordance with the degree distribution [11][12][13]. In this structure, which is commonly termed as the "onion structure" at present, almost all nodes are connected with nodes with the same degree and the degree correlation between nearest neighbor nodes is positively maximal.…”

Section: Introductionmentioning

confidence: 99%

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Robustness analysis of bimodal networks in the whole range of degree correlation

Mizutaka

Tanizawa

2016

Phys. Rev. E

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We present exact analysis of the physical properties of bimodal networks specified by the two peak degree distribution fully incorporating the degree-degree correlation between node connection. The structure of the correlated bimodal network is uniquely determined by the Pearson coefficient of the degree correlation, keeping its degree distribution fixed. The percolation threshold and the giant component fraction of the correlated bimodal network are analytically calculated in the whole range of the Pearson coefficient from −1 to 1 against two major types of node removal, which are the random failure and the degree-based targeted attack. The Pearson coefficient for next-nearestneighbor pairs is also calculated, which always takes a positive value even when the correlation between nearest-neighbor pairs is negative. From the results, it is confirmed that the percolation threshold is a monotonically decreasing function of the Pearson coefficient for the degrees of nearestneighbor pairs increasing from −1 and 1 regardless of the types of node removal. In contrast, the node fraction of the giant component for bimodal networks with positive degree correlation rapidly decreases in the early stage of random failure, while that for bimodal networks with negative degree correlation remains relatively large until the removed node fraction reaches the threshold. In this sense, bimodal networks with negative degree correlation are more robust against random failure than those with positive degree correlation.

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“…of complex systems itself is indeed a classical problem [1]. Essential theoretical findings those have been found on this issue include the general instability of large and densely interacting systems [2], the self-organized criticality [3], and the relation between the robustness and the network structure of the systems [4,5]. However, the key and universal feature of the real complex systems, openness, has not been well considered.…”

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confidence: 99%

Do Connections Make Systems Robust? A New Scenario for the Complexity-Stability Relation

Shimada

Murase

Ito

2015

Proceedings of the International Conference on Social Modeling and Simulation, Plus Econophysics Colloquium 2014

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Whether interactions among the elements make the system robust or fragile has been a central issue in broad range of field. Here we introduce a novel type of mechanism which governs the robustness of open and dynamical systems such as social and economical systems, based on a very simple mathematical model. This mechanism suggest a moderate number ( 10) of interactions per element is optimal to make the system against successive and unpredictable disturbances. The relation between this very simple model and more detailed nonlinear dynamical models is discussed, to emphasize the relevance of this newly reported mechanism to the real phenomena.

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Onion-like network topology enhances robustness against malicious attacks

Cited by 155 publications

References 23 publications

Combined Heuristic Attack Strategy on Complex Networks

Combined Heuristic Attack Strategy on Complex Networks

Robustness analysis of bimodal networks in the whole range of degree correlation

Do Connections Make Systems Robust? A New Scenario for the Complexity-Stability Relation

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