Related papers: Percolation and epidemics in a two-dimensional sma…
Recent studies introduced biased (degree-dependent) edge percolation as a model for failures in real-life systems. In this work, such process is applied to networks consisting of two types of nodes with edges running only between nodes of…
In the real world, many complex systems interact with other systems. In addition, the intra- or inter-systems for the spread of information about infectious diseases and the transmission of infectious diseases are often not random, but with…
In this paper we study the diffusion of an SIS-type epidemics on a network under the presence of a random environment, that enters in the definition of the infection rates of the nodes. Accordingly, we model the infection rates in the form…
On a geometric model for complex networks (introduced by Krioukov et al.) we investigate the bootstrap percolation process. This model consists of random geometric graphs on the hyperbolic plane having $N$ vertices, a dependent version of…
Accessibility percolation is a new type of percolation problem inspired by evolutionary biology. To each vertex of a graph a random number is assigned and a path through the graph is called accessible if all numbers along the path are in…
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),…
The problem of continuum percolation in dispersions of rods is reformulated in terms of weighted random geometric graphs. Nodes (or sites or vertices) in the graph represent spatial locations occupied by the centers of the rods. The…
We consider cumulative merging percolation (CMP), a long-range percolation process describing the iterative merging of clusters in networks, depending on their mass and mutual distance. For a specific class of CMP processes, which…
We provide an explicit solution of the problem of level-set percolation for multivariate Gaussians defined in terms of weighted graph Laplacians on complex networks. The solution requires an analysis of the heterogeneous micro-structure of…
We propose a model for epidemic spreading on a finite complex network with a restriction to at most one contamination per time step. Because of a highly discrete character of the process, the analysis cannot use the continous approximation,…
We assume that the state of a number of nodes in a network could be investigated if necessary, and study what configuration of those nodes could facilitate a better solution for the diffusion-source-localization (DSL) problem. In…
The social percolation model \citep{solomon-et-00} considers a 2-dimensional regular lattice. Each site is occupied by an agent with a preference $x_{i}$ sampled from a uniform distribution $U[0,1]$. Agents transfer the information about…
A simple but powerful network model with $n$ nodes and $m$ partly overlapping layers is generated as an overlay of independent random graphs $G_1,\dots,G_m$ with variable sizes and densities. The model is parameterised by a joint…
The Susceptible-Infected-Recovered (SIR) model is studied in multilayer networks with arbitrary number of links across the layers. By following the mapping to bond percolation we give the analytical expression for the epidemic threshold and…
The effective, fast transport of matter through porous media is often characterized by complex dispersion effects. To describe in mathematical terms such situations, instead of a simple macroscopic equation (as in the classical Darcy's…
We present simulation results for the contact process on regular, cubic networks that are composed of a one-dimensional lattice and a set of long edges with unbounded length. Networks with different sets of long edges are considered, that…
The propagation of model epidemics on a small-world network under the action of immunization is studied. Although the connectivity in this kind of networks is rather uniform, a vaccination strategy focused on the best connected individuals…
We introduce the simplest model which relates the emergence of collective social/economic phenomena to the existence of a (possibly self-organized) percolation transition. We suggest a series of extensions to financial, economic, political…
In this work we investigate the problem of estimating the percolation centrality of every vertex in a graph. This centrality measure quantifies the importance of each vertex in a graph going through a contagious process. It is an open…
Modeling the spread of infections on networks is a well-studied and important field of research. Most infection and diffusion models require a real value or probability on the edges of the network as an input, but this is rarely available…