Network robustness of multiplex networks with interlayer degree correlations

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

doi:10.1103/physreve.89.042811

Cited by 228 publications

(227 citation statements)

References 44 publications

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“…4, for supporting numerical experiments). Other interrelation descriptors, such as the commonly used degree correlation [34][35][36][37], do not necessarily yield similar results ( [29], A.iv., Fig. 5).…”

Section: -3mentioning

confidence: 99%

Exact coupling threshold for structural transition reveals diversified behaviors in interconnected networks

2015

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An interconnected network features a structural transition between two regimes [F. Radicchi and A. Arenas, Nat. Phys. 9, 717 (2013)]: one where the network components are structurally distinguishable and one where the interconnected network functions as a whole. Our exact solution for the coupling threshold uncovers network topologies with unexpected behaviors. Specifically, we show conditions that superdiffusion, introduced by Gómez et al. [Phys. Rev. Lett. 110, 028701 (2013) Fig. 1, where the interconnection strength between the layers is parametrized by a coupling weight p > 0. Radicchi and Arenas [16] demonstrated the existence of a structural transition point p * . Depending on the coupling weight p between the two networks, the collective interconnected network can function in two regimes: if p < p * , the two networks are structurally distinguishable; whereas if p > p * , they behave as a whole.While studying diffusion processes on the same type of interconnected network in Fig. 1, Gomez et al. [14] observed superdiffusion: for sufficiently large p, the diffusion in the interconnected network takes place faster than in either of the networks separately. Superdiffusion arises due to the synergistic effect of the network interconnection and exemplifies a characteristic phenomenon in interconnected networks. Placement of the introduction point of superdiffusion with respect to the critical point p * is missing in the literature.Whereas the existence of a critical transition p * was reported in [16], here, we determine the exact coupling threshold p * . Our exact solution illuminates the role of each individual * Corresponding author: faryad@ksu.edu network component and their combined configuration on the structural transition phenomena and uncovers unexpected behaviors. Specifically, we show structural transition is not a necessary condition for achieving superdiffusion. Indeed, superdiffusion can be achieved for a coupling weight p even below the structural transition threshold p * , which is surprising because, intuitively, synergy is not expected if the network components are functioning distinctly. Moreover, we observe that the structural transition disappears when one of the network components has vanishing algebraic connectivity [18][19][20], as is the case for a class of scalefree networks. Therefore, components of such interconnected network topologies become indistinguishable despite very weak coupling between them.Spectral analysis plays a key role in understanding interconnected networks. Hernandez et al. [21] found the complete spectra of interconnected networks with identical components. studied the interconnection of more than two networks with an arbitrary oneto-one correspondence structure. employed eigenvalue interlacing [18] to provide bounds for the Laplacian spectra of an interconnected network with a general interconnection pattern. In addition, in a similar context of structural transition as [16], D'Agostino [24] showed that adding interconnection links among networks causes st...

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Section: -3mentioning

confidence: 99%

Exact coupling threshold for structural transition reveals diversified behaviors in interconnected networks

2015

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“…The percolation phase transition describing the emergence of the MCGC in multilayer networks, with layers formed by random networks with given degree distributions, has been fully characterized as a discontinuous and hybrid transition [11,12]. The phase transition remains hybrid and discontinuous in the presence of correlations in the degrees of replica nodes [28] but can become a continuous in the case of partial interdependence [29][30][31] or if some nodes are not active (not connected) in each layer [10,32]. Interestingly, these results can be obtained using a locally treelike approximation, or equivalently, a message passing algorithm that admits an epidemic spreading interpretation [13,36].…”

Section: Introductionmentioning

confidence: 99%

“…The emergence of the MCGC has been studied on a variety of multilayer structures including multiplex networks [11][12][13][28][29][30][31][32] and networks of networks [33][34][35]. Networks of networks are multilayer networks formed by different networks (layers), where the nodes of different networks might be related by interdependencies.…”

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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“…In fact they are very often characterized by a significant overlap of the links in different layers 5,7,25,26 , by correlations between the degree of the same node in different layers 10,27 , by the heterogeneous activity (presence of a node in a layer) of the nodes in different layers 6,28 and by a significant overlap of the communities in different layers 29,30 . These correlations can be exploited to extract relevant information from multiplex network structures that cannot be inferred by analyzing single layers taken in isolation or the aggregated network where all the interactions are taken at the same level.…”

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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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Network robustness of multiplex networks with interlayer degree correlations

Cited by 228 publications

References 44 publications

Exact coupling threshold for structural transition reveals diversified behaviors in interconnected networks

Exact coupling threshold for structural transition reveals diversified behaviors in interconnected networks

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

Extracting information from multiplex networks

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