Related papers: Numerical assessment of the percolation threshold …
The convergence between effective medium theory and pore-network modelling is examined. Electrical conductance on two and three-dimensional cubic resistor networks is used as an example of transport through composite materials or porous…
Percolation in an information-theoretically secure graph is considered where both the legitimate and the eavesdropper nodes are distributed as Poisson point processes. For both the path-loss and the path-loss plus fading model, upper and…
The site percolation problem is one of the core topics in statistical physics. Evaluation of the percolation threshold, which separates two phases (sometimes described as conducting and insulating), is useful for a range of problems from…
These lectures give an introduction to the methods of conformal field theory as applied to deriving certain results in two-dimensional critical percolation: namely the probability that there exists at least one cluster connecting two…
We study the effect of assortative and disassortative mixing on the robustness of networks under random node failures. For ordinary (dyadic) networks, by using the generating function technique and stochastic simulations, we show that the…
In this work we demonstrate the ability of the Minimal Spanning Tree to duplicate the information contained within a percolation analysis for a point dataset. We show how to construct the percolation properties from the Minimal Spanning…
A great deal of effort has been spent measuring topological features of the Internet. However, it was recently argued that sampling based on taking paths or traceroutes through the network from a small number of sources introduces a…
Network science is a rapidly expanding field, with a large and growing body of work on network-based dynamical processes. Most theoretical results in this area rely on the so-called \emph{locally tree-like approximation}. This is, however,…
We analyze critical phenomena on networks generated as the union of hidden variables models (networks with any desired degree sequence) with arbitrary graphs. The resulting networks are general small-worlds similar to those a` la Watts and…
The fractions of samples spanning a lattice at its percolation threshold are found by computer simulation of random site-percolation in two- and three-dimensional hypercubic lattices using different boundary conditions. As a byproduct we…
In the present article, numerical simulations have been performed to find the bond and site percolation thresholds on two-dimensional Gabriel graphs (GG) for Poisson point processes. GGs belong to the family of proximity graphs and are…
A new ``Percolation with Clustering'' (PWC) model is introduced, where (the probabilities of) site percolation configurations on the leaf set of a binary tree are rewarded exponentially according to a generic function, which measures the…
In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially…
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…
In this paper we study the interplay between epidemic spreading and risk perception on multiplex networks. The basic idea is that the effective infection probability is affected by the perception of the risk of being infected, which we…
In this paper we study the macroscopic conduction properties of large but finite binary networks with conducting bonds. By taking a combination of a spectral and an averaging based approach we derive asymptotic formulae for the conduction…
We present a model supported by simulation to explain the effect of temperature on the conduction threshold in disordered systems. Arrays with randomly distributed local thresholds for conduction occur in systems ranging from…
In high dimensional percolation at parameter $p < p_c$, the one-arm probability $\pi_p(n)$ is known to decay exponentially on scale $(p_c - p)^{-1/2}$. We show the same statement for the ratio $\pi_p(n) / \pi_{p_c}(n)$, establishing a form…
Classical blockmodel is known as the simplest among models of networks with community structure. The model can be also seen as an extremely simply example of interconnected networks. For this reason, it is surprising that the percolation…
In this paper, we study the robustness of network topologies. We use the concept of percolation as measuring tool to assess the reliability polynomial of those systems which can be modeled as a general inhomogeneous random graph as well as…