Percolation in multiplex networks with overlap

Cellai, Davide; López, Eduardo; Zhou, Jie; Gleeson, James P.; Bianconi, Ginestra

doi:10.1103/physreve.88.052811

Cited by 191 publications

(201 citation statements)

References 42 publications

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“…Therefore, it is of crucial importance to determine the robustness of multiplex networks in the presence of this structural feature. In order to model multiplex networks with link overlap, the notion of multilinks [9,37,42] turns out to be extremely useful. Two nodes i and j are connected by a multilink m = (m 1 ,m 2 , .…”

Section: Multiplex Network With Link Overlapmentioning

confidence: 99%

“…V we present the multilink definitions in the case of link overlap, using the formalism of Ref. [42]. In Sec.…”

Section: Introductionmentioning

confidence: 99%

“…The second approach is instead based only on a traditional local treelike approximation [41]. 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.…”

Section: Introductionmentioning

confidence: 99%

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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: Multiplex Network With Link Overlapmentioning

confidence: 99%

“…V we present the multilink definitions in the case of link overlap, using the formalism of Ref. [42]. In Sec.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2016

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“…Similarly, in biological systems basic constituents such as proteins can have physical, co-localization, genetic or many other types of interactions. Recently, it has been shown that retaining such multi-dimensional information 7 and modelling the structure of interdependent and multilayer systems respectively through interdependent 8 and multilayer networks [9][10][11][12] reveals new nontrivial structural properties [13][14][15][16][17][18][19][20] and relevant emergent physical phenomena [21][22][23][24][25][26][27] .…”

mentioning

confidence: 99%

Structural reducibility of multilayer networks

et al. 2015

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Many complex systems can be represented as networks consisting of distinct types of interactions, which can be categorized as links belonging to different layers. For example, a good description of the full protein-protein interactome requires, for some organisms, up to seven distinct network layers, accounting for different genetic and physical interactions, each containing thousands of protein-protein relationships. A fundamental open question is then how many layers are indeed necessary to accurately represent the structure of a multilayered complex system. Here we introduce a method based on quantum theory to reduce the number of layers to a minimum while maximizing the distinguishability between the multilayer network and the corresponding aggregated graph. We validate our approach on synthetic benchmarks and we show that the number of informative layers in some real multilayer networks of protein-genetic interactions, social, economical and transportation systems can be reduced by up to 75%.

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“…Recent studies alone this line include empirical analysis of real-world network data [11,12], evolution of network structures [13][14][15], and new critical phenomena and processes occurring on them [9,10,16,17]. These coupled networks exhibit some common features, such as the inter degree-degree correlation [18], inter-similarity [19], multiple dependence in providing support [9], and node and edge overlapping between layers [20]. These features have important effects on critical phenomena and the dynamics, including percolation [9], cascading failure [16], diffusion processes [21], emergence of cooperation [22] and epidemic dynamics [17], when compared with those in a single network.…”

Section: Introductionmentioning

confidence: 99%

Suppressed epidemics in multirelational networks

Wang

Cai

et al. 2015

Phys. Rev. E

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A two-state epidemic model in networks with links mimicking two kinds of relationships between connected nodes is introduced. Links of weights w1 and w0 occur with probabilities p and 1 − p, respectively. The fraction of infected nodes ρ(p) shows a non-monotonic behavior, with ρ drops with p for small p and increases for large p. For small to moderate w1/w0 ratios, ρ(p) exhibits a minimum that signifies an optimal suppression. For large w1/w0 ratios, the suppression leads to an absorbing phase consisting only of healthy nodes within a range pL ≤ p ≤ pR, and an active phase with mixed infected and healthy nodes for p < pL and p > pR. A mean field theory that ignores spatial correlation is shown to give qualitative agreement and capture all the key features. A physical picture that emphasizes the intricate interplay between infections via w0 links and within clusters formed by nodes carrying the w1 links is presented. The absorbing state at large w1/w0 ratios results when the clusters are big enough to disrupt the spread via w0 links and yet small enough to avoid an epidemic within the clusters. A theory that uses the possible local environments of a node as variables is formulated. The theory gives results in good agreement with simulation results, thereby showing the necessity of including longer spatial correlations.

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Percolation in multiplex networks with overlap

Cited by 191 publications

References 42 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

Structural reducibility of multilayer networks

Suppressed epidemics in multirelational networks

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