Epidemic threshold in directed networks

Liu, Cong; Wang, Huijuan; Mieghem, Piet Van

doi:10.1103/physreve.88.062802

Cited by 52 publications

(41 citation statements)

References 53 publications

(75 reference statements)

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“…Incorporating the adjacency matrix, the quench meanfield (QMF) approach is widely used to study the spreading dynamics. Note that other approaches also use the adjacency matrix to describe network topology, including the discretetime Markov chain approach [86] and the N -intertwined approach [87,88]. At time t a susceptible node i is infected by its neighbors with a probability β N j=1 A ij ρ j (t), where ρ j (t) = 1 − s j (t) is the probability that neighboring node j of node i is in the infected state at time t. Thus the evolution of ρ i (t) can be expressed…”

Section: A General Framework For Models Of Epidemic Spreadingmentioning

confidence: 99%

Unification of theoretical approaches for epidemic spreading on complex networks

et al. 2017

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Models of epidemic spreading on complex networks have attracted great attention among researchers in physics, mathematics, and epidemiology due to their success in predicting and controlling scenarios of epidemic spreading in real-world scenarios. To understand the interplay between epidemic spreading and the topology of a contact network, several outstanding theoretical approaches have been developed. An accurate theoretical approach describing the spreading dynamics must take both the network topology and dynamical correlations into consideration at the expense of increasing the complexity of the equations. In this short survey we unify the most widely used theoretical approaches for epidemic spreading on complex networks in terms of increasing complexity, including the mean-field, the heterogeneous mean-field, the quench mean-field, dynamical messagepassing, link percolation, and pairwise approximation. We build connections among these approaches to provide new insights into developing an accurate theoretical approach to spreading dynamics on complex networks.

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Section: A General Framework For Models Of Epidemic Spreadingmentioning

confidence: 99%

Unification of theoretical approaches for epidemic spreading on complex networks

et al. 2017

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“…Note that this differs from the technique presented in Ref. [33] in that we choose two bidirectional links instead of two random links that may also contain unidirectional links so that the directionality increases after each step. Then, we choose two unidirectional links, one from each bidirectional link, and rewire them as follows.…”

Section: A Directionality-increasing Rewiring (Dir)mentioning

confidence: 99%

“…[38], and also employed by Ref. [33]. Here, we improve it to gradually increase the directionality, via a technique we call directionality-increasing rewiring (DIR).…”

Section: A Directionality-increasing Rewiring (Dir)mentioning

confidence: 99%

“…Inspired by earlier research on directed networks [31,[33][34][35][36][37], we propose two algorithms to construct directed networks. One is a rewiring algorithm that can be applied to any existing undirected network to obtain a directed network with any given directionality, but each node has the same in-degree and out-degree as the original undirected network.…”

Section: Algorithm Descriptionmentioning

confidence: 99%

“…Directed networks are important because many realworld networks, e.g., Twitter, Facebook, and email networks, are directed [33]. In contrast to undirected networks, directed networks contain unidirectional links.…”

Section: Introductionmentioning

confidence: 99%

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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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Interdependence of Resistance and Optical Transmission in Conductive Nanowire Networks

Ainsworth

Derby

Sampson

2018

Advcd Theory and Sims

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Metallic nanowire networks show great potential for use in transparent conductive displays. The coupled relationship between the principal materials properties of interest for such applications, optical transmittance and sheet resistance, is known to be affected by both nanowire dimensions and area coverage. Existing theory to describe the observed interdependence requires consideration of both bulk and surface phases. Here, an analysis of structural variables in these materials is presented confirming that bulk considerations do not typically apply. Accordingly, a model using statistical theory for random line networks is developed that requires consideration of a surface phase only. The resultant simple expression relates sheet resistance and optical transmission of heterogeneous nanowire assemblies in terms of nanowire dimensions. Comparison of our model with experimental and simulation data from the literature shows excellent agreement. In closing, theoretical insights into the observed influence on sheet resistance of polydisperse nanowire lengths and structural variability are provided.

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Epidemic threshold in directed networks

Cited by 52 publications

References 53 publications

Unification of theoretical approaches for epidemic spreading on complex networks

Unification of theoretical approaches for epidemic spreading on complex networks

Nonconsensus opinion model on directed networks

Interdependence of Resistance and Optical Transmission in Conductive Nanowire Networks

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