Related papers: Bootstrap percolation on spatial networks
Percolation establishes the connectivity of complex networks and is one of the most fundamental critical phenomena for the study of complex systems. On simple networks, percolation displays a second-order phase transition; on multiplex…
Most social, technological and biological networks are embedded in a finite dimensional space, and the distance between two nodes influences the likelihood that they link to each other. Indeed, in social systems, the chance that two…
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…
In the polluted bootstrap percolation model, the vertices of a graph are independently declared initially occupied with probability p or closed with probability q. At subsequent steps, a vertex becomes occupied if it is not closed and it…
In modified two-neighbour bootstrap percolation in two dimensions each site of $\mathbb Z^2$ is initially independently infected with probability $p$ and on each discrete time step one additionally infects sites with at least two…
We study the random connection model on hyperbolic space $\mathbb{H}^d$ in dimension $d=2,3$. Vertices of the spatial random graph are given as a Poisson point process with intensity $\lambda>0$. Upon variation of $\lambda$ there is a…
We study the statistics of the backbone cluster between two sites separated by distance $r$ in two-dimensional percolation networks subjected to spatial long-range correlations. We find that the distribution of backbone mass follows the…
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),…
Motivated by an application in wireless telecommunication networks, we consider a two-type continuum-percolation problem involving a homogeneous Poisson point process of users and a stationary and ergodic point process of base stations.…
The self-consistent probabilistic approach has proven itself powerful in studying the percolation behavior of interdependent or multiplex networks without tracking the percolation process through each cascading step. In order to understand…
In long-range percolation on $\mathbb{Z}^d$, points $x$ and $y$ are connected by an edge with probability $1-\exp(-\beta\|x-y\|^{-d-\alpha})$, where $\alpha>0$ is fixed and $\beta \geq 0$ is a parameter. As $d$ and $\alpha$ vary, the model…
A random hopping on a fractal network with dimension slightly above one, $d = 1 + \epsilon$, is considered as a model of transport for conducting polymers with nonmetallic conductivity. Within the real space renormalization group method of…
Bond percolation on infinite heavy-tailed power-law random networks lacks a proper phase transition; or one may say, there is a phase transition at {\em zero percolation probability}. Nevertheless, a finite size percolation threshold…
The critical phase of bond percolation on the random growing tree is examined. It is shown that the root cluster grows with the system size $N$ as $N^\psi$ and the mean number of clusters with size $s$ per node follows a power function $n_s…
$k$-core percolation is a percolation model which gives a notion of network functionality and has many applications in network science. In analysing the resilience of a network under random damage, an extension of this model is introduced,…
We describe the critical window for percolation in the universality class of sparse growing random graphs. In our models, vertices arrive sequentially and connect independently to each earlier vertex $v$ with probability proportional to a…
Consider the following model of strong-majority bootstrap percolation on a graph. Let r be some positive integer, and p in [0,1]. Initially, every vertex is active with probability p, independently from all other vertices. Then, at every…
The combination of the compactness of networks, featuring small diameters, and their complex architectures results in a variety of critical effects dramatically different from those in cooperative systems on lattices. In the last few years,…
In a recent Letter, Friedman and Landsberg discussed the underlying mechanism of explosive phase transitions on complex networks [Phys. Rev. Lett. 103, 255701 (2009)]. This Brief Report presents a modest, though more insightful extension of…
We study the effects of mobility on two crucial characteristics in multi-scale dynamic networks: percolation and connection times. Our analysis provides insights into the question, to what extent long-time averages are well-approximated by…