Towards real-world complexity: an introduction to multiplex networks

Lee, Kyu Min; Min, Byungjoon; Goh, K.-I.

doi:10.1140/epjb/e2015-50742-1

Cited by 178 publications

(115 citation statements)

References 176 publications

(369 reference statements)

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“…Multilayer networks [1][2][3] describe complex systems formed by different interacting networks. Examples of multilayer networks are ubiquitous, ranging from infrastructures and transportation networks to cellular and brain networks [4][5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Message passing theory for percolation models on multiplex networks with link overlap

2016

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Multiplex networks describe a large variety of complex systems, including infrastructures, transportation networks, and biological systems. Most of these networks feature a significant link overlap. It is therefore of particular importance to characterize the mutually connected giant component in these networks. Here we provide a message passing theory for characterizing the percolation transition in multiplex networks with link overlap and an arbitrary number of layers M. Specifically we propose and compare two message passing algorithms that generalize the algorithm widely used to study the percolation transition in multiplex networks without link overlap. The first algorithm describes a directed percolation transition and admits an epidemic spreading interpretation. The second algorithm describes the emergence of the mutually connected giant component, that is the percolation transition, but does not preserve the epidemic spreading interpretation. We obtain the phase diagrams for the percolation and directed percolation transition in simple representative cases. We demonstrate that for the same multiplex network structure, in which the directed percolation transition has nontrivial tricritical points, the percolation transition has a discontinuous phase transition, with the exception of the trivial case in which all the layers completely overlap.

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Section: Introductionmentioning

confidence: 99%

Message passing theory for percolation models on multiplex networks with link overlap

2016

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“…where σ k [α] is the standard deviation of degrees in layer 30 α [15,29]. The value of this Pearson correlation coefficient 31 between the two layers is r = 0.271, which indicates weak 32 positive correlation [21].…”

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confidence: 99%

Weighted multiplex network of air transportation

Вaргa

2016

Eur. Phys. J. B

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Abstract. In several real networks large heterogeneity of links is present either in intensity or in the nature of relationships. Therefore, recent studies in network science indicate that more detailed topological information are available if weighted or multi-layer aspect is applied. In the age of globalization air transportation is a representative example of huge complex infrastructure systems, which has been analyzed form different points of view. In this paper a novel approach is applied to study the airport network as a weighted multiplex taking into account the fact that the rules and fashion of domestic and international flights differ. Restricting study to only topological features and their correlations in the system (disregarding traffic) one can see reasons why simple network approximation is not adequate.

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“…20,21 Several researches have shown that the topological features of a layer are indeed a®ected by the shape of other layers in multiplex networks. 18,19,22 In other words, the traditional link prediction methods only take into account the topological information derived from the single-layer networks (called the intralayer information) but neglect the additional information originated from other layers in multiplex networks (called the interlayer information). From the macroperspective point of view, if a multiplex network is treated as an integrated network, the interactions between nodes in di®erent layers can be regarded as the overall structural features of these nodes in di®erent aspects.…”

Section: Introductionmentioning

confidence: 99%

Link prediction via layer relevance of multiplex networks

Yao

Zhang

Yang

et al. 2017

Int. J. Mod. Phys. C

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In complex networks, the existing link prediction methods primarily focus on the internal structural information derived from single-layer networks. However, the role of interlayer information is hardly recognized in multiplex networks, which provide more diverse structural features than single-layer networks. Actually, the structural properties and functions of one layer can a®ect that of other layers in multiplex networks. In this paper, the e®ect of interlayer structural properties on the link prediction performance is investigated in multiplex networks. By utilizing the intralayer and interlayer information, we propose a novel \Node Similarity Index" based on \Layer Relevance" (NSILR) of multiplex network for link prediction. The performance of NSILR index is validated on each layer of seven multiplex networks in real-world systems. Experimental results show that the NSILR index can signi¯cantly improve the prediction performance compared with the traditional methods, which only consider the intralayer information. Furthermore, the more relevant the layers are, the higher the performance is enhanced.

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Towards real-world complexity: an introduction to multiplex networks

Cited by 178 publications

References 176 publications

Message passing theory for percolation models on multiplex networks with link overlap

Message passing theory for percolation models on multiplex networks with link overlap

Weighted multiplex network of air transportation

Link prediction via layer relevance of multiplex networks

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