Giant components in directed multiplex networks

Azimi-Tafreshi, N.; Dorogovtsev, S. N.; Mendes, J. F. F.

doi:10.1103/physreve.90.052809

Cited by 15 publications

(24 citation statements)

References 25 publications

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“…The nature of this phase transition is a clear sign that multilayer networks with interdependencies display a significant fragility with respect to random damage. Several other generalized percolation problems on multiplex networks have been also proposed, including competition between the layers [20,21], weak percolation [22,23], generalized k-core percolation [24], percolation on directed multiplex networks [25], spanning connectivity [26], and bond percolation [27].…”

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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“…Examples include metabolic networks and gene regulatory networks in biological systems (23), transportation networks and power grids in infrastructure systems (24,25), and citation networks and trust networks in social systems (26). Directed multiplex networks with a giant strongly connected component (GSCC) are significantly more vulnerable than those with a giant weakly connected component (GWCC) (27).…”

mentioning

confidence: 99%

Breakdown of interdependent directed networks

Liu

Stanley

Gao

2016

Proc. Natl. Acad. Sci. U.S.A.

139

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Increasing evidence shows that real-world systems interact with one another via dependency connectivities. Failing connectivities are the mechanism behind the breakdown of interacting complex systems, e.g., blackouts caused by the interdependence of power grids and communication networks. Previous research analyzing the robustness of interdependent networks has been limited to undirected networks. However, most real-world networks are directed, their in-degrees and out-degrees may be correlated, and they are often coupled to one another as interdependent directed networks. To understand the breakdown and robustness of interdependent directed networks, we develop a theoretical framework based on generating functions and percolation theory. We find that for interdependent Erd} os-Rényi networks the directionality within each network increases their vulnerability and exhibits hybrid phase transitions. We also find that the percolation behavior of interdependent directed scale-free networks with and without degree correlations is so complex that two criteria are needed to quantify and compare their robustness: the percolation threshold and the integrated size of the giant component during an entire attack process. Interestingly, we find that the in-degree and out-degree correlations in each network layer increase the robustness of interdependent degree heterogeneous networks that most real networks are, but decrease the robustness of interdependent networks with homogeneous degree distribution and with strong coupling strengths. Moreover, by applying our theoretical analysis to real interdependent international trade networks, we find that the robustness of these real-world systems increases with the in-degree and out-degree correlations, confirming our theoretical analysis.interdependent networks | directed networks | degree correlations | percolation theory

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“…Our model is as follows. A multilayer network consists of M co-existing networks G (1) , G (2) , . .…”

Section: Introductionmentioning

confidence: 99%

On a Class of Stochastic Multilayer Networks

Jiang

Nain

Towsley

et al. 2019

SIGMETRICS Perform. Eval. Rev.

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In this paper, we introduce a new class of stochastic multilayer networks. A stochastic multilayer network is the aggregation of M networks (one per layer) where each is a subgraph of a foundational network G. Each layer network is the result of probabilistically removing links and nodes from G. The resulting network includes any link that appears in at least K layers. This model is an instance of a non-standard site-bond percolation model. Two sets of results are obtained: first, we derive the probability distribution that the M-layer network is in a given configuration for some particular graph structures (explicit results are provided for a line and an algorithm is provided for a tree), where a configuration is the collective state of all links (each either active or inactive). Next, we show that for appropriate scalings of the node and link selection processes in a layer, links are asymptotically independent as the number of layers goes to infinity, and follow Poisson distributions. Numerical results are provided to highlight the impact of having several layers on some metrics of interest (including expected size of the cluster a node belongs to in the case of the line). This model finds applications in wireless communication networks with multichannel radios, multiple social networks with overlapping memberships, transportation networks, and, more generally, in any scenario where a common set of nodes can be linked via co-existing means of connectivity.

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Giant components in directed multiplex networks

Cited by 15 publications

References 25 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

Breakdown of interdependent directed networks

On a Class of Stochastic Multilayer Networks

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