Related papers: Percolation transition in networks with degree-deg…
We introduce a correlated static model and investigate a percolation transition. The model is a modification of the static model and is characterized by assortative degree-degree correlation. As one varies the edge density, the network…
We provide arguments for the property of the degree-degree correlations of giant components formed by the percolation process on uncorrelated random networks. Using the generating functions, we derive a general expression for the…
As a fundamental structural transition in complex networks, core percolation is related to a wide range of important problems. Yet, previous theoretical studies of core percolation have been focusing on the classical Erd\H{o}s-R\'enyi…
We reconsider the problem of percolation on an equilibrium random network with degree-degree correlations between nearest-neighboring vertices focusing on critical singularities at a percolation threshold. We obtain criteria for…
We propose a maximally disassortative (MD) network model which realizes a maximally negative degree-degree correlation, and study its percolation transition to discuss the effect of a strong degree-degree correlation on the percolation…
Mixing patterns in large self-organizing networks, such as the Internet, the World Wide Web, social and biological networks are often characterized by degree-degree {dependencies} between neighbouring nodes. One of the problems with the…
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…
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…
In complex networks the degrees of adjacent nodes may often appear dependent -- which presents a modelling challenge. We present a working framework for studying networks with an arbitrary joint distribution for the degrees of adjacent…
Scale-free networks, in which the distribution of the degrees obeys a power-law, are ubiquitous in the study of complex systems. One basic network property that relates to the structure of the links found is the degree assortativity, which…
We study the effects of the degree-degree correlations on the pressure congestion J when we apply a dynamical process on scale free complex networks using the gradient network approach. We find that the pressure congestion for…
We study the percolation phase transition in hierarchical scale-free nets. Depending on the method of construction, the nets can be fractal or small-world (the diameter grows either algebraically or logarithmically with the net size),…
Complex networks display various types of percolation transitions. We show that the degree distribution and the degree-degree correlation alone are not sufficient to describe diverse percolation critical phenomena. This suggests that a…
We provide a simple proof that graphs in a general class of self-similar networks have zero percolation threshold. The considered self-similar networks include random scale-free graphs with given expected node degrees and zero clustering,…
We present a simple model of network growth and solve it by writing down the dynamic equations for its macroscopic characteristics like the degree distribution and degree correlations. This allows us to study carefully the percolation…
We discuss the behavior of large ensembles of phase oscillators networking via scale-free topologies in the presence of a positive correlation between the oscillators' natural frequencies and network's degrees. In particular, we show that…
We propose that negative degree correlation among nodes in a network of nonlinear oscillators, often detected in real world networks, is motivated by its positive effects on synchronizability. In so doing, we use a novel methodology to…
Recent work on the internet, social networks, and the power grid has addressed the resilience of these networks to either random or targeted deletion of network nodes. Such deletions include, for example, the failure of internet routers or…
Percolation, the formation of a macroscopic connected component, is a key feature in the description of complex networks. The dynamical properties of a variety of systems can be understood in terms of percolation, including the robustness…
Networks facilitate the spread of cascades, allowing a local perturbation to percolate via interactions between nodes and their neighbors. We investigate how network structure affects the dynamics of a spreading cascade. By accounting for…