Weighted Multiplex Networks

Menichetti, Giulia; Remondini, Daniel; Panzarasa, Pietro; Mondragón, Raúl J.; Bianconi, Ginestra

doi:10.1371/journal.pone.0097857

Cited by 199 publications

(241 citation statements)

References 37 publications

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“…The vast majority of multiplex networks in infrastructures, transport, social, and collaboration networks are characterized by significant link overlap [4,7,9]. Therefore, it is of crucial importance to determine the robustness of multiplex networks in the presence of this structural feature.…”

Section: Multiplex Network With Link Overlapmentioning

confidence: 99%

“…Therefore, it is of crucial importance to determine the robustness of multiplex networks in the presence of this structural feature. In order to model multiplex networks with link overlap, the notion of multilinks [9,37,42] turns out to be extremely useful. Two nodes i and j are connected by a multilink m = (m 1 ,m 2 , .…”

Section: Multiplex Network With Link Overlapmentioning

confidence: 99%

“…Numerous multilayer networks have a significant link overlap [4,7,9,37], which explains the need to explore the percolation transition on this type of correlated multilayer structures [38]. Recently, two approaches were used to describe the transition in duplex networks (i.e.,, networks formed by M = 2 layers) with link overlap.…”

Section: Introductionmentioning

confidence: 99%

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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: Multiplex Network With Link Overlapmentioning

confidence: 99%

Section: Multiplex Network With Link Overlapmentioning

confidence: 99%

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

2016

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“…To this end we constructed a citation-collaboration multiplex formed by the authors of the Physical Review E (PRE) journal 7 . The dataset includes all the papers published on PRE from 1993 to 2009.…”

Section: Case Studies a Multiplex Pagerank Analysis Of The Physimentioning

confidence: 99%

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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“…In fact, both quantities have been already used to characterize the eigenfunctions of the adjacency matrices of random network models (see some examples in Refs. [31,36,39,42,48,[53][54][55][56][57][66][67][68][69]). …”

Section: B Entropic Eigenfunction Localization Lengthmentioning

confidence: 99%

Universality in the spectral and eigenfunction properties of random networks

et al. 2015

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By the use of extensive numerical simulations we show that the nearest-neighbor energy level spacing distribution P (s) and the entropic eigenfunction localization length of the adjacency matrices of Erdős-Rényi (ER) fully random networks are universal for fixed average degree ξ ≡ αN (α and N being the average network connectivity and the network size, respectively). We also demonstrate that Brody distribution characterizes well P (s) in the transition from α = 0, when the vertices in the network are isolated, to α = 1, when the network is fully connected. Moreover, we explore the validity of our findings when relaxing the randomness of our network model and show that, in contrast to standard ER networks, ER networks with diagonal disorder also show universality. Finally, we also discuss the spectral and eigenfunction properties of small-world networks.

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Weighted Multiplex Networks

Cited by 199 publications

References 37 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

Extracting information from multiplex networks

Universality in the spectral and eigenfunction properties of random networks

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