Eigenvector centrality of nodes in multiplex networks

Solá, Luis; Romance, Miguel; Criado, Regino; Flores, Julio; Amo, Alejandro García del; Boccaletti, Stefano

doi:10.1063/1.4818544

Cited by 245 publications

(192 citation statements)

References 30 publications

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“…Finally also the community structure of networks in different layer might be correlated, with communities defined in different layers overlapping with each other. Inference problems on multiplex networks, including the determination of centrality measures for nodes [31][32][33] and the characterization of the multiplex network mesoscale structure 29,30,[35][36][37][38] , can take advantage of these correlations to extract more information from these datasets. In this way a clear path is defined for extracting relevant information from multiplex network structures, which cannot be unveiled by analyzing its single layers taken in isolation or its aggregated description.…”

Section: Structural Multiplex Measures a Multiplex Networkmentioning

confidence: 99%

“…Quantifying the centrality of the nodes in multiplex networks is a fundamental problem that in these last years has attracted increasing attention from the network science community [31][32][33] . Among the different proposed centrality measures, the Multiplex PageRank 32 can be used to assess how the centrality of a node in a single layer is affected by the centrality of the same node in another layer.…”

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confidence: 99%

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Extracting information from multiplex networks

Iacovacci

Bianconi

2016

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Multiplex networks are generalized network structures that are able to describe networks in which the same set of nodes are connected by links that have different connotations. Multiplex networks are ubiquitous since they describe social, financial, engineering and biological networks as well. Extending our ability to analyze complex networks to multiplex network structures increases greatly the level of information that is possible to extract from Big Data. For these reasons characterizing the centrality of nodes in multiplex networks and finding new ways to solve challenging inference problems defined on multiplex networks are fundamental questions of network science. In this paper we discuss the relevance of the Multiplex PageRank algorithm for measuring the centrality of nodes in multilayer networks and we characterize the utility of the recently introduced indicator function Θ S for describing their mesoscale organization and community structure. As working examples for studying these measures we consider three multiplex network datasets coming for social science.Multilayer networks are formed by nodes connected by links describing interactions with different connotations. When the same set of nodes can be connected by different types of links, the resulting multilayer network, is also called a multiplex network. Most social networks are multiplex, since the same set of people might be connected by different types of social ties or might communicate through different means of communication. As networks are ultimately a way to encode information about a complex set of interactions one of the most pressing and challenging problem in network science is to extract relevant information from them. Here we show evidence that the Multiplex PageRank algorithm and the recently introduced indicator function Θ S are able to extract from multiplex networks an information than cannot be inferred by analyzing the single layers taken in isolation or the aggregated network in which links of different type are not distinguished.The vast majority of complex interacting systems, from social networks to the brain and the biological networks of the cell, are multilayer networks 1-3 . Multilayer networks are formed by several networks (layers) describing interactions of different nature and connotation. Therefore multilayer networks encode significant more information than the network which include all the interactions of the multilayer network but does not distinguishes between the different nature of the links. As a consequence of this, one the most pressing challenge in multiplex network theory is devising algorithms and numerical methods to extract relevant information from these network structures. a) Electronic mail: j.iacovacci@qmul.ac.uk b) Electronic mail: g.bianconi@qmul.ac.uk Multilayer networks can be distinguished in two wide classes: multiplex networks and networks of networks 1,3 . Network of networks are multilayer networks formed by layers constituted by different nodes. Examples of network of networks are comple...

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Section: Structural Multiplex Measures a Multiplex Networkmentioning

confidence: 99%

mentioning

confidence: 99%

Extracting information from multiplex networks

Iacovacci

Bianconi

2016

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…Similarly, in biological systems basic constituents such as proteins can have physical, co-localization, genetic or many other types of interactions. Recently, it has been shown that retaining such multi-dimensional information 7 and modelling the structure of interdependent and multilayer systems respectively through interdependent 8 and multilayer networks [9][10][11][12] reveals new nontrivial structural properties [13][14][15][16][17][18][19][20] and relevant emergent physical phenomena [21][22][23][24][25][26][27] .…”

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confidence: 99%

Structural reducibility of multilayer networks

et al. 2015

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Many complex systems can be represented as networks consisting of distinct types of interactions, which can be categorized as links belonging to different layers. For example, a good description of the full protein-protein interactome requires, for some organisms, up to seven distinct network layers, accounting for different genetic and physical interactions, each containing thousands of protein-protein relationships. A fundamental open question is then how many layers are indeed necessary to accurately represent the structure of a multilayered complex system. Here we introduce a method based on quantum theory to reduce the number of layers to a minimum while maximizing the distinguishability between the multilayer network and the corresponding aggregated graph. We validate our approach on synthetic benchmarks and we show that the number of informative layers in some real multilayer networks of protein-genetic interactions, social, economical and transportation systems can be reduced by up to 75%.

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“…New multiplex datasets [9][10][11][12][13][14] and multiplex network measures have been introduced in order to quantify their complexity. Examples of such measures are the overlap [11,13,14] of the links in different layers, the interdependence [12,15] that extends the concept of betweenness centrality to multiplexes, or the centrality measures [16,17]. Many dynamical processes have been defined on multiplexes, including cascades of failure in interdependent networks [18][19][20][21][22], antagonistic percolation [23], dynamical cascades [24], diffusion [25], epidemic spreading [26], election models [27], game theory [28,29], etc.…”

Section: Introductionmentioning

confidence: 99%

Emergence of overlap in ensembles of spatial multiplexes and statistical mechanics of spatial interacting network ensembles

2014

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Spatial networks range from the brain networks, to transportation networks and infrastructures. Recently interacting and multiplex networks are attracting great attention because their dynamics and robustness cannot be understood without treating at the same time several networks. Here we present maximal entropy ensembles of spatial multiplex and spatial interacting networks that can be used in order to model spatial multilayer network structures and to build null models of real datasets. We show that spatial multiplexes naturally develop a significant overlap of the links, a noticeable property of many multiplexes that can affect significantly the dynamics taking place on them. Additionally, we characterize ensembles of spatial interacting networks and we analyze the structure of interacting airport and railway networks in India, showing the effect of space in determining the link probability.

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Eigenvector centrality of nodes in multiplex networks

Cited by 245 publications

References 30 publications

Extracting information from multiplex networks

Extracting information from multiplex networks

Structural reducibility of multilayer networks

Emergence of overlap in ensembles of spatial multiplexes and statistical mechanics of spatial interacting network ensembles

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