<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>k</mml:mi><mml:mtext>−</mml:mtext><mml:mi>core</mml:mi></mml:mrow></mml:math>percolation on multiplex networks

Azimi-Tafreshi, N.; Gómez‐Gardeñes, Jesús; Dorogovtsev, S. N.

doi:10.1103/physreve.90.032816

Cited by 112 publications

(112 citation statements)

References 36 publications

(42 reference statements)

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“…Mean cascade size ρ To investigate threshold dynamics on multiplex networks with heterogeneous layer responses, we first present the analytical approach for calculating the mean cascade size, applicable to multiplex networks with sparse, locally-treelike layers. The analytic approach developed for the threshold cascade model on single-layer networks [17] can be generalized to the case of multiplex networks with -layers (" -plex networks") [5] by following a mean-field-type reasoning similar to other models on multiplex networks [2,12,13].…”

Section: Analytical Approachmentioning

confidence: 99%

Threshold cascades with response heterogeneity in multiplex networks

2014

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Threshold cascade models have been used to describe spread of behavior in social networks and cascades of default in financial networks. In some cases, these networks may have multiple kinds of interactions, such as distinct types of social ties or distinct types of financial liabilities; furthermore, nodes may respond in different ways to influence from their neighbors of multiple types. To start to capture such settings in a stylized way, we generalize a threshold cascade model to a multiplex network in which nodes follow one of two response rules: some nodes activate when, in at least one layer, a large enough fraction of neighbors are active, while the other nodes activate when, in all layers, a large enough fraction of neighbors are active. Varying the fractions of nodes following either rule facilitates or inhibits cascades. Near the inhibition regime, global cascades appear discontinuously as the network density increases; however, the cascade grows more slowly over time. This behavior suggests a way in which various collective phenomena in the real world could appear abruptly yet slowly.

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Section: Analytical Approachmentioning

confidence: 99%

Threshold cascades with response heterogeneity in multiplex networks

2014

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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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“…In these cases the aforementioned functional equation remains the main bottleneck and is typically addressed numerically with the only exception of percolation studies. Some percolation criteria were obtained analytically both in directed networks (in and out percolation [8] and weak percolation [11]) and in multiplex networks (k-core percolation [13], weak percolation [16], a strong mutually connected component [12], and a giant connected component [20]). To date, few results are available on the size distribution of finite connected components in these configuration models.…”

Section: Introductionmentioning

confidence: 99%

Finite connected components in infinite directed and multiplex networks with arbitrary degree distributions

Kryven

2017

Phys. Rev. E

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Finite connected components in infinite directed and multiplex networks with arbitrary degree distributions Kryven, I. General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. This work presents exact expressions for size distributions of weak and multilayer connected components in two generalizations of the configuration model: networks with directed edges and multiplex networks with an arbitrary number of layers. The expressions are computable in a polynomial time and, under some restrictions, are tractable from the asymptotic theory point of view. If first partial moments of the degree distribution are finite, the size distribution for two-layer connected components in multiplex networks exhibits an exponent − 3 2 in the critical regime, whereas the size distribution of weakly connected components in directed networks exhibits two critical exponents − .

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k−corepercolation on multiplex networks

Cited by 112 publications

References 36 publications

Threshold cascades with response heterogeneity in multiplex networks

Threshold cascades with response heterogeneity in multiplex networks

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

Finite connected components in infinite directed and multiplex networks with arbitrary degree distributions

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