Related papers: Percolation in Directed Scale-Free Networks

We describe the anomalous phase transition of the emergence of the giant connected component in scale-free networks growing under mechanism of preferential linking. We obtain exact results for the size of the giant connected component and…

Introduced recently, the concept of hierarchical degree allows a more complete characterization of the topological context of a node in a complex network than the traditional node degree. This article presents analytical characterization…

Recently, new results on percolation of interdependent networks have shown that the percolation transition can be first order. In this paper we show that, when considering antagonistic interactions between interacting networks, the…

We extend the merging model for undirected networks by Kim et al. [Eur. Phys. J. B 43, 369 (2004)] to directed networks and investigate the emerging scale-free networks. Two versions of the directed merging model, friendly and hostile…

We study the temporal percolation properties of temporal networks by taking as a representative example the recently proposed activity driven network model [N. Perra et al., Sci. Rep. 2, 469 (2012)]. Building upon an analytical framework…

Percolation is a fundamental concept that brought new understanding on the robustness properties of complex systems. Here we consider percolation on weakly interacting networks, that is, network layers coupled together by much less…

We give several algebraic bounds for percolation on directed and undirected graphs: proliferation of strongly-connected clusters, proliferation of in- and out-clusters, and the transition associated with the number of giant components.

In many real network systems, nodes usually cooperate with each other and form groups, in order to enhance their robustness to risks. This motivates us to study a new type of percolation, group percolation, in interdependent networks under…

The entropy of network ensembles characterizes the amount of information encoded in the network structure, and can be used to quantify network complexity, and the relevance of given structural properties observed in real network datasets…

Fractal scale-free networks are empirically known to exhibit disassortative degree mixing. It is, however, not obvious whether a negative degree correlation between nearest neighbor nodes makes a scale-free network fractal. Here we examine…

We discuss how various models of scale-free complex networks approach their limiting properties when the size N of the network grows. We focus mainly on equilibrated networks and their finite-size degree distributions. Our results show that…

Many real-world networks exhibit scale-free feature, have a small diameter and a high clustering tendency. We have studied the properties of a growing network, which has all these features, in which an incoming node is connected to its…

In this study, we investigate bond percolation in networks that have the Poisson degree distribution and a nearest-neighbor degree-degree correlation. Previous numerical studies on percolation critical behaviors of degree-correlated…

In this work we investigate the spectra of Laplacian matrices that determine many dynamic properties of scale-free networks below and at the percolation threshold. We use a replica formalism to develop analytically, based on an integral…

The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in…

The stochastic addition of either vertices or connections in a network leads to the observation of the percolation transition, a structural change with the appearance of a connected component encompassing a finite fraction of the system.…

We present an exact mathematical framework able to describe site-percolation transitions in real multiplex networks. Specifically, we consider the average percolation diagram valid over an infinite number of random configurations where…

Very often, when studying topological or dynamical properties of random scale-free networks, it is tacitly assumed that degree-degree correlations are not present. However, simple constraints, such as the absence of multiple edges and…

The use of degree-degree correlations to model realistic networks which are characterized by their Pearson's coefficient, has become widespread. However the effect on how different correlation algorithms produce different results on…

Delaunay triangulation can be considered as a type of complex networks. For complex networks, the degree distribution is one of the most important inherent characteristics. In this paper, we first consider the two- and three-dimensional…