Related papers: Condensation in preferential attachment models wit…
We identify the upper large deviation probability for the number of edges in scale-free geometric random graph models as the space volume goes to infinity. Our result covers the models of scale-free percolation, the Boolean model with…
A preferential attachment model for a growing network incorporating deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step $t=1,2,\ldots$, with probability $\pi_1>0$ a new vertex with one…
We investigate structural properties of large, sparse random graphs through the lens of "sampling convergence" (Borgs et. al. (2017)). Sampling convergence generalizes left convergence to sparse graphs, and describes the limit in terms of a…
We study the dynamics of condensation for a stochastic continuous mass transport process defined on a one-dimensional lattice. Specifically we introduce three different variations of the truncated random average process. We generalize…
In an affiliation network vertices are linked to attributes and two vertices are declared adjacent whenever they share a common attribute. For example, two customers of an internet shop are called adjacent if they have purchased the same or…
We extend the work of Antunovi\'{c}, Mossel and R\'{a}cz on competing types in preferential attachment models to include cases where the types have different fitnesses, which may be either multiplicative or additive. We will show that,…
We study the following preferential attachment variant of the classical Erdos-Renyi random graph process. Starting with an empty graph on n vertices, new edges are added one-by-one, and each time an edge is chosen with probability roughly…
Several lattice models display a condensation transition in real space when the density of a suitable order parameter exceeds a critical value. We consider one of such models with two conservation laws, in a one-dimensional open setup where…
The spatial preferred attachment (SPA) model is a model for networked information spaces such as domains of the World Wide Web, citation graphs, and on-line social networks. It uses a metric space to model the hidden attributes of the…
We are interested in the structure of large Bienaym\'e-Galton-Watson random trees whose offspring distribution is critical and falls within the domain of attraction of a stable law of index $\alpha=1$. In stark contrast to the case $\alpha…
Prediction and control of network dynamics are grand-challenge problems in network science. The lack of understanding of fundamental laws driving the dynamics of networks is among the reasons why many practical problems of great…
We introduce a new model of competition on growing networks. This extends the preferential attachment model, with the key property that node choices evolve simultaneously with the network. When a new node joins the network, it chooses…
In this paper we present a framework for the extension of the preferential attachment (PA) model to heterogeneous complex networks. We define a class of heterogeneous PA models, where node properties are described by fixed states in an…
In the coevolution of network structures and opinion formation, we investigate the effects of a mixed population with distinctive relinking preferences on both the convergence time and the network structures. It has been found that a…
The lattice gas model of condensation in a heterogeneous pore system, represented by a random graph of cells, is studied using an exact analytical solution. A binary mixture of pore cells with different coordination numbers is shown to…
We investigate particle condensation in a driven pair exclusion process on one- and two- dimensional lattices under the periodic boundary condition. The model describes a biased hopping of particles subject to a pair exclusion constraint…
We study the evolution of an initially random distribution of particles on a square lattice, under certain rules for `growing' and `culling' of particles. In one version we allow the particles to move laterally along the surface (mobile…
We investigate a class of growing graphs embedded into the $d$-dimensional torus where new vertices arrive according to a Poisson process in time, are randomly placed in space and connect to existing vertices with a probability depending on…
One of the best-known models in network science is preferential attachment. In this model, the probability of attaching to a node depends on the degree of all nodes in the population, and thus depends on global information. In many…
We study Anderson localisation on high-dimensional graphs with spatial structure induced by long-ranged but distance-dependent hopping. To this end, we introduce a class of models that interpolate between the short-range Anderson model on a…