Cohen, Erez, ben-Avraham, and Havlin Reply:

Cohen, Reuven; Erez, Keren; ben‐Avraham, Daniel; Havlin, Shlomo

doi:10.1103/physrevlett.87.219802

Cited by 497 publications

(931 citation statements)

References 4 publications

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“…Scale-free networks are known to be sensitive to the removal of highly connected nodes [25][26][27][28][29]. However, the existence of a giant connected component in the network does not depend on the presence of highly connected nodes and can be present even after the removal of a significant number of nodes [29,30].…”

Section: Attack-induced Cascades In Complex Networkmentioning

confidence: 99%

Attacks and Cascades in Complex Networks

Lai

Motter

Nishikawa

2004

Lecture Notes in Physics

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Abstract. This paper reviews two problems in the security of complex networks: cascades of overload failures on nodes and range-based attacks on links. Cascading failures have been reported for numerous networks and refer to the subsequent failure of other parts of the network induced by the failure of or attacks on only a few nodes. We investigate a mechanism leading to cascades of overload failures in complex networks by constructing a simple model incorporating the flow of physical quantities in the network. The second problem is motivated by the fact that most existing works on security of complex networks consider attacks on nodes rather than on links. We address attacks on links. Our investigation leads to the finding that many scale-free networks are more sensitive to attacks on short-range than on long-range links. Besides its importance concerning network security, our result has the unexpected implication that the small-world phenomenon in these scale-free networks is mainly due to short-range links.

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Section: Attack-induced Cascades In Complex Networkmentioning

confidence: 99%

Attacks and Cascades in Complex Networks

Lai

Motter

Nishikawa

2004

Lecture Notes in Physics

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“…For example, for binomial networks, 3 ξ can be changed from 0 to 1 when ρ = 1, but the minimum value of ξ must be approximately 0.3 and any smaller ξ value is disallowed when ρ = 0. We explore the relation between the minimal possible directionality ξ and a given in-degree and out-degree correlation ρ first via numerical simulations 4 in both binomial and SF networks. 5 Figure 3(b) shows the linear relationship in both types of network.…”

Section: B Constructing An Asymmetric In-degree and Out-degree Netwomentioning

confidence: 99%

“…Social scientists began refining the empirical study of networks in the 1970s, and many of the mathematical and physical tools currently used in network science were originally developed by them [1]. Social network science has been used to understand the diffusion of innovations, news, and rumors as well as the spread of disease and health-related human behavior [2][3][4][5][6][7][8][9]. The decades-old hot topic of opinion dynamics continues to be a central focus among researchers attempting to understand the opinion formation process.…”

Section: Introductionmentioning

confidence: 99%

Nonconsensus opinion model on directed networks

Havlin

Stanley

et al. 2014

Phys. Rev. E

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Dynamic social opinion models have been widely studied on undirected networks, and most of them are based on spin interaction models that produce a consensus. In reality, however, many networks such as Twitter and the World Wide Web are directed and are composed of both unidirectional and bidirectional links. Moreover, from choosing a coffee brand to deciding who to vote for in an election, two or more competing opinions often coexist. In response to this ubiquity of directed networks and the coexistence of two or more opinions in decision-making situations, we study a nonconsensus opinion model introduced by Shao et al. [Phys. Rev. Lett. 103, 018701 (2009)] on directed networks. We define directionality ξ as the percentage of unidirectional links in a network, and we use the linear correlation coefficient ρ between the in-degree and out-degree of a node to quantify the relation between the in-degree and out-degree. We introduce two degree-preserving rewiring approaches which allow us to construct directed networks that can have a broad range of possible combinations of directionality ξ and linear correlation coefficient ρ and to study how ξ and ρ impact opinion competitions. We find that, as the directionality ξ or the in-degree and out-degree correlation ρ increases, the majority opinion becomes more dominant and the minority opinion's ability to survive is lowered.

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“…Today, it evolves to one of the worldwide large scale systems, whose topology belongs to a SF network with a power-law degree distribution [29]. The SF nature of the Internet exhibits both error tolerance and attack vulnerability [4,5,6,28]. Moreover, the geographical constraints on the topological linkings [8,9] implicitly affect the robustness, indeed, the numerical study [4] has been shown more serious result in the Internet than that in a relational SF network called Barabási-Albert model without geographical constraints.…”

Section: Simulation For As Networkmentioning

confidence: 99%

“…Another fact is the scale-free (SF) structure that follows a power-law degree distribution P (k) ∼ k −γ , 2 < γ < 3, consists of many nodes with low degrees and a few hubs with high degrees. The heterogeneous networks are drastically broken into many isolated clusters, when only a small fraction of high degree nodes are removed as the intentional attacks [4,5]. However, the SF structure is robust against random failures [4,6], and well balanced in the meaning of both economical and efficient communication by small number of hops in a connected network as few links as possible [7].…”

Section: Introductionmentioning

confidence: 99%

Improvement of the robustness on geographical networks by adding shortcuts

Hayashi

Matsukubo

2007

Physica A: Statistical Mechanics and its Applications

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In a topological structure affected by geographical constraints on liking, the connectivity is weakened by constructing local stubs with small cycles, a something of randomness to bridge them is crucial for the robust network design. In this paper, we numerically investigate the effects of adding shortcuts on the robustness in geographical scale-free network models under a similar degree distribution to the original one. We show that a small fraction of shortcuts is highly contribute to improve the tolerance of connectivity especially for the intentional attacks on hubs. The improvement is equivalent to the effect by fully rewirings without geographical constraints on linking. Even in the realistic Internet topologies, these effects are virtually examined.

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Cohen, Erez, ben-Avraham, and Havlin Reply:

Cited by 497 publications

References 4 publications

Attacks and Cascades in Complex Networks

Attacks and Cascades in Complex Networks

Nonconsensus opinion model on directed networks

Improvement of the robustness on geographical networks by adding shortcuts

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