The structure and dynamics of multilayer networks

Boccaletti, S.; Bianconi, G.; Criado, R.; del Genio, C. I.; Gómez-Gardeñes, J.; Romance, M.; Sendiña-Nadal, I.; Wang, Z.; Zanin, M.

doi:10.48550/arxiv.1407.0742

Cited by 8 publications

(15 citation statements)

References 293 publications

(486 reference statements)

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“…Then the condition for a node to be viable becomes whether the supernode to which it belongs is connected with other viable supernodes through each and every type of (non-overlapping) links attached to some nodes within the supernode. To take this into account, it is convenient to "renomalize" the network by regarding each overlap cluster as a single supernode, 3 which are connected via non-overlapping links connecting nodes in different supernodes. This approach was first proposed for the percolation of interdependent networks with link overlap in Ref.…”

Section: Analytic Solution For CD Algorithm With Link Overlapmentioning

confidence: 99%

“…Many real-world complex systems ranging from society to critical infrastructure operate through multiple layers of distinct interactions among constituents as well as the interplay between these interaction layers [1,2,3]. Multiplex network [4] is a class of networks introduced to model such systems, in which the same set of nodes (say, individuals in a society) are connected via more than one type of links (say friendships, kinships, co-workerships, etc).…”

Section: Introductionmentioning

confidence: 99%

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Link overlap, viability, and mutual percolation in multiplex networks

Min

Lee

et al. 2015

Chaos, Solitons & Fractals

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Many real-world complex systems are best modeled by multiplex networks. The multiplexity has proved to have broad impact on the system's structure and function. Most theoretical studies on multiplex networks to date, however, have largely ignored the effect of link overlap across layers despite strong empirical evidences for its significance. In this article, we investigate the effect of link overlap in the viability of multiplex networks, both analytically and numerically. Distinctive role of overlapping links in viability and mutual connectivity is emphasized and exploited for setting up proper analytic framework. A rich phase diagram for viability is obtained and greatly diversified patterns of hysteretic behavior in viability are observed in the presence of link overlap. Mutual percolation with link overlap is revisited as a limit of multiplex viability problem, and controversy between existing results is clarified. The distinctive role of overlapping links is further demonstrated by the different responses of networks under random removals of overlapping and non-overlapping links, respectively, as well as under several removal strategies. Our results show that the link overlap strongly facilitates viability and mutual percolation; at the same time, the presence of link overlap poses challenge in analytical approach to the problem.

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Section: Analytic Solution For CD Algorithm With Link Overlapmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Link overlap, viability, and mutual percolation in multiplex networks

Min

Lee

et al. 2015

Chaos, Solitons & Fractals

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“…This method can be applied to the precise determination of epidemic threshold on various networks, and could be extended to other dynamic processes such as information diffusion and behavior spreading. Further work should be done to check the effectiveness of this method on more complicated networks (e.g., temporal networks [51] and multilayer networks [52]), and the cases in asynchronous updating scheme also need to be investigated. Besides, the accurate analytic approximation of the epidemic threshold for general networks remains an important problem.…”

Section: Discussionmentioning

confidence: 99%

Simulated identification of epidemic threshold on finite-size networks

Shu,

Wang,

Tang

et al. 2014

Preprint

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Epidemic threshold is one of the most important features of the epidemic dynamics. Through a lot of numerical simulations in classic Susceptible-Infected-Recovered (SIR) and Susceptible-Infected-Susceptible (SIS) models on various types of networks, we study the simulated identification of epidemic thresholds on finite-size networks. We confirm that the susceptibility measure goes awry for the SIR model due to the bimodal distribution of outbreak sizes near the critical point, while the simulated thresholds of the SIS and SIR models can be accurately determined by analyzing the peak of the epidemic variability. We further verify the accuracy of theoretical predictions derived by the heterogeneous meanfield theory (HMF) and the quenched mean-field theory (QMF), by comparing them with the simulated threshold of the SIR model obtained from the variability measure. The results show that the HMF prediction agrees very well with the simulated threshold, except the case that the networks are disassortive, in which the QMF prediction is more close to the simulated threshold.

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“…Multi-layer flow networks (MFN) can be regarded as a special type of multi-layer networks [14,15]. This tool is able to well depict multiplex flows in different layers.…”

Section: A Modeling Multi-layer Flow Networkmentioning

confidence: 99%

Exploring multi-layer flow network of international trade based on flow distances

Shen,

Zhang,

Zheng

2015

Preprint

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Based on the approach of flow distances, the international trade flow system is studied from the perspective of multi-layer flow network. A model of multi-layer flow network is proposed for modelling and analyzing multiple types of flows in flow systems. Then, flow distances are introduced, and symmetric minimum flow distance is presented. Subsequently, we discuss the establishment of the multi-layer flow networks of international trade from two coupled viewpoints, i.e., the viewpoint of commodity flow and that of money flow. Thus, the multi-layer flow networks of international trade is explored. First, trading "trophic levels" are adopted to depict positions that economies occupied in the flow network. We find that the distributions of trading "trophic levels" have the similar clustering pattern for different types of commodity, and there are some regularities between money flow network and commodity flow network. Second, we find that active and competitive countries trade a wide spectrum of products, while inactive and underdeveloped countries trade a limited variety of products. Besides, some abnormal countries import many types of goods, which the vast majority of countries do not need to import. It may indicate an abnormal economic status. Third, harmonic node centrality is proposed and we find the phenomenon of centrality stratification. It means that competitive countries tend to occupy the central positions in the trading of a large variety of commodities, while underdeveloped countries likely in the peripheral positions in the trading of their limited varieties of products. Fourth, we find that manufactured products have significant larger mean first-passage flow distances from the source to the sink than that of primary products.

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The structure and dynamics of multilayer networks

Cited by 8 publications

References 293 publications

Link overlap, viability, and mutual percolation in multiplex networks

Link overlap, viability, and mutual percolation in multiplex networks

Simulated identification of epidemic threshold on finite-size networks

Exploring multi-layer flow network of international trade based on flow distances

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