Weak percolation on multiplex networks

Baxter, G. J.; Dorogovtsev, S. N.; Mendes, J. F. F.; Cellai, Davide

doi:10.1103/physreve.89.042801

Cited by 66 publications

(86 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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%

“…Interestingly, it turns out that a message passing algorithm that admits an epidemic spreading interpretation [42,43], inspired by the algorithm originally proposed for multiplex network without link overlap, does not capture the MCGC [39][40][41], but instead characterizes a new type of directed percolation. This process can be interpreted as a variation of a bootstrap percolation dynamics [22,44] or as the viability percolation problem [40] in the limit in which the resource nodes are vanishing. Here we call this dynamical process directed percolation and its order parameter directed mutually connected giant component (DMCGC) to distinguish it from the MCGC.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

2016

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2016

Self Cite

View full text Add to dashboard Cite

show abstract

“…The joint degree distribution for uniform growth with β1 = 3 and β2 = 3. Theoretical result is presented in (17). Since the values decay fast in k and , we have depicted the logarithm of the inverse of this function, for a smoother output and better visibility.…”

Section: Model 2: Uniform Attachment In Two Layersmentioning

confidence: 99%

“…These new theoretical measures enable studying various phenomena on top of multiplex networks analytically. Examples include epidemics [12,13], pathogen-awareness interplay [14,15], percolation processes [12,16,17], random walks [18,19], evolution of cooperation [20][21][22][23], diffusion processes [24] and social contagion [25]. For thorough reviews, see [23,26,27].…”

Section: Introductionmentioning

confidence: 99%

Growing multiplex networks with arbitrary number of layers

Momeni

Fotouhi

2015

Phys. Rev. E

View full text Add to dashboard Cite

This paper focuses on the problem of growing multiplex networks. Currently, the results on the joint degree distribution of growing multiplex networks present in the literature pertain to the case of two layers, and are confined to the special case of homogeneous growth, and are limited to the state state (that is, the limit of infinite size). In the present paper, we obtain closed-form solutions for the joint degree distribution of heterogeneously growing multiplex networks with arbitrary number of layers in the steady state. Heterogeneous growth means that each incoming node establishes different numbers of links in different layers. We consider both uniform and preferential growth. We then extend the analysis of the uniform growth mechanism to arbitrary times. We obtain a closedform solution for the time-dependent joint degree distribution of a growing multiplex network with arbitrary initial conditions. Throughout, theoretical findings are corroborated with Monte Carlo simulations. The results shed light on the effects of the initial network on the transient dynamics of growing multiplex networks, and takes a step towards characterizing the temporal variations of the connectivity of growing multiplex networks, as well as predicting their future structural properties.

show abstract

“…Previously, undirected multiplex networks were explored [10,[12][13][14][15][16][17][18][19][20][21][22]. In the present article, we study multiplex networks, in which all edges are directed.…”

Section: Introductionmentioning

confidence: 99%

Giant components in directed multiplex networks

2014

View full text Add to dashboard Cite

We describe the complex global structure of giant components in directed multiplex networks which generalizes the well-known bow-tie structure, generic for ordinary directed networks. By definition, a directed multiplex network contains vertices of one type and directed edges of m different types. In directed multiplex networks, we distinguish a set of different giant components based on the existence of directed paths of different types between their vertices, such that for each type of edges, the paths run entirely through only edges of that type. If, in particular, m = 2, we define a strongly viable component as a set of vertices, in which for each type of edges, each two vertices are interconnected by at least two directed paths in both directions, running through the edges of only this type. We show that in this case, a directed multiplex network contains, in total, 9 different giant components including the strongly viable component. In general, the total number of giant components is 3 m . For uncorrelated directed multiplex networks, we obtain exactly the size and the emergence point of the strongly viable component and estimate the sizes of other giant components.

show abstract

Weak percolation on multiplex networks

Cited by 66 publications

References 35 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

Growing multiplex networks with arbitrary number of layers

Giant components in directed multiplex networks

Contact Info

Product

Resources

About