2014
DOI: 10.1103/physreve.90.032816
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kcorepercolation on multiplex networks

Abstract: We generalize the theory of k-core percolation on complex networks to k-core percolation on multiplex networks, where k≡(k(1),k(2),...,k(M)). Multiplex networks can be defined as networks with vertices of one kind but M different types of edges, representing different types of interactions. For such networks, the k-core is defined as the largest subgraph in which each vertex has at least k(i) edges of each type, i=1,2,...,M. We derive self-consistency equations to obtain the birth points of the k-cores and the… Show more

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Cited by 112 publications
(112 citation 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%
“…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%
“…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%
“…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%