Related papers: The contact process on dynamical scale-free networ…
We introduce a very general model of an inhomogenous random graph with independence between the edges, which scales so that the number of edges is linear in the number of vertices. This scaling corresponds to the p=c/n scaling for G(n,p)…
In this paper we introduce a contact process on a dynamical long range percolation (CPDLP) defined on a complete graph $(V,\mathcal{E})$. A dynamical long range percolation is a Feller process defined on the edge set $\mathcal{E}$, which…
We present the distance matrix evolution for different types of networks: exponential, scale-free and classical random ones. Statistical properties of these matrices are discussed as well as topological features of the networks. Numerical…
We study the contact process running in the one-dimensional lattice undergoing dynamical percolation, where edges open at rate $vp$ and close at rate $v(1-p)$. Our goal is to explore how the speed of the environment, $v$, affects the…
We present an analysis of the classical contact process on scale-free networks. A mean-field study, both for finite and infinite network sizes, yields an absorbing-state phase transition at a finite critical value of the control parameter,…
The paper is concerned with the interplay between network structure and traffic dynamics in a communications network, from the viewpoint of end-to-end performance of packet transfer. We use a model of network generation that allows the…
The Watts-Strogatz algorithm of transferring the square lattice to a small world network is modified by introducing preferential rewiring constrained by connectivity demand. The evolution of the network is two-step: sequential preferential…
The long-time dynamics of the 1D contact process suddenly brought out of an uncorrelated initial state is studied through a light-cone transfer-matrix renormalisation group approach. At criticality, the system undergoes ageing which is…
Many real-world scale-free networks, such as neural networks and online communication networks, consist of a fixed number of nodes but exhibit dynamic edge fluctuations. However, traditional models frequently overlook scenarios where the…
The contact process on an infinite homogeneous tree is shown to exhibit at least two phase transitions as the infection parameter lambda is varied. For small values of lambda a single infection eventually dies out. For larger lambda the…
We analyze random networks that change over time. First we analyze a dynamic Erdos-Renyi model, whose edges change over time. We describe its stationary distribution, its convergence thereto, and the SI contact process on the network, which…
The contact process is a particular case of birth-and-death processes on infinite particle configurations. We consider the contact models on locally compact separable metric spaces. We prove the existence of a one-parameter set of invariant…
We study the two-species symbiotic contact process (2SCP), recently proposed in [de Oliveira, Santos and Dickman, Phys. Rev. E {\bf 86}, 011121 (2012)] . In this model, each site of a lattice may be vacant or host single individuals of…
The exponential family of random graphs is one of the most promising class of network models. Dependence between the random edges is defined through certain finite subgraphs, analogous to the use of potential energy to provide dependence…
We study the discrete-time threshold-$\theta \geq 2$ contact process on random graphs of general degrees. For random graphs with a given degree distribution $\mu$, we show that if $\mu$ is lower bounded by $\theta+2$ and has finite $k$th…
We study a pulse-coupled dynamics of excitable elements in uncorrelated scale-free networks. Regimes of self-sustained activity are found for homogeneous and inhomogeneous couplings, in which the system displays a wide variety of behaviors,…
Scale-free networks contain many small cliques and cycles. We model such networks as inhomogeneous random graphs with regularly varying infinite-variance weights. For these models, the number of cliques and cycles have exact integral…
A random graph evolution based on the interactions of N vertices is studied. During the evolution both the preferential attachment method and the uniform choice of vertices are allowed. The weight of a vertex means the number of its…
Contact processes describe the transmission of distinct properties of nodes via the links of a network. They provide a simple framework for many phenomena, such as epidemic spreading and opinion formation. Combining contact processes with…
This article proposes methods to model nonstationary temporal graph processes. This corresponds to modelling the observation of edge variables (relationships between objects) indicating interactions between pairs of nodes (or objects)…