Bond Percolation on Multiplex Networks

Hackett, Adam; Cellai, Davide; Gómez, Sergio; Arenas, Àlex; Gleeson, James P.

doi:10.1103/physrevx.6.021002

Cited by 78 publications

(84 citation statements)

References 47 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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“…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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“…Figure 2(a) shows that time-delays produce temporal microtransitions, i.e., R(t) versus t exhibits multiple transitions, which also exist in percolation [44][45][46]. When no individuals have time-delays i.e., when f=0.0, the behavior adoption R(t) versus time t grows continuously.…”

Section: Time-delays With Dirac Delta Distributionmentioning

confidence: 99%

Effects of time-delays in the dynamics of social contagions

2018

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Time-delays are pervasive in such real-world complex networks as social contagions and biological systems, and they radically alter the evolution of the dynamic processes in networks. We use a non-Markovian spreading threshold model to study the effects of time-delays on social contagions. Using extensive numerical simulations and theoretical analyses we find that relatively long time-delays induce a microtransition in the evolution of a fraction of recovered individuals, i.e., the fraction of recovered individuals versus time exhibits multiple phase transitions. The microtransition is sharper and more obvious when high-degree individuals have a higher probability of experiencing timedelays, and the microtransition is obscure when the time-delay distribution reaches heterogeneity. We use an edge-based compartmental theory to analyze our research and find that the theoretical results agree well with our numerical simulation results.

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Bond Percolation on Multiplex Networks

Cited by 78 publications

References 47 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

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

Effects of time-delays in the dynamics of social contagions

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