相关论文: A central limit theorem for the number of isolated…

Preferential attachment graphs are random graphs designed to mimic properties of typical real world networks. They are constructed by a random process that iteratively adds vertices and attaches them preferentially to vertices that already…

We consider a general preferential attachment model, where the probability that a newly arriving vertex connects to an older vertex is proportional to a sublinear function of the indegree of the older vertex at that time. It is well known…

We study logical limit laws for preferential attachment random graphs. In this random graph model, vertices and edges are introduced recursively: at time $1$, we start with vertices $0,1$ and $m$ edges between them. At step $n+1$ the vertex…

We consider an evolving preferential attachment random graph model where at discrete times a new node is attached to an old node, selected with probability proportional to a superlinear function of its degree. For such schemes, it is known…

For a family of linear preferential attachment graphs, we provide rates of convergence for the total variation distance between the degree of a randomly chosen vertex and an appropriate power law distribution as the number of vertices tends…

We consider the number of crossings in a random embedding of a graph, $G$, with vertices in convex position. We give explicit formulas for the mean and variance of the number of crossings as a function of various subgraph counts of $G$.…

For a sequence of random graphs, the limit law we refer to is the existence of a limiting probability of any graph property that can be expressed in terms of predicate logic. A zero-one limit law is shown by Shelah and Spencer for…

Paper proposes a model of large networks based on a random preferential attachment graph with addition of complete subgraphs (cliques). The proposed model refers to models of random graphs following the nonlinear preferential attachment…

We study a random graph $G_n$, which combines aspects of geometric random graphs and preferential attachment. The resulting random graphs have power-law degree sequences with finite mean and possibly infinite variance. In particular, the…

In this article, we derive Stein's method for approximating a spatial random graph by a generalised random geometric graph, which has vertices given by a finite Gibbs point process and edges based on a general connection function. Our main…

In this work we consider a growing random graph sequence where a new vertex is less likely to join to an existing vertex with high degree and more likely to join to a vertex with low degree. In contrast to the well studied…

The preferential attachment network with fitness is a dynamic random graph model. New vertices are introduced consecutively and a new vertex is attached to an old vertex with probability proportional to the degree of the old one multiplied…

In this paper we investigate geometric properties of graphs generated by a preferential attachment random graph model with edge-steps. More precisely, at each time $t\in\mathbb{N}$, with probability $p$ a new vertex is added to the graph (a…

We provide optimal rates of convergence to the asymptotic distribution of the (properly scaled) degree of a fixed vertex in two preferential attachment random graph models. Our approach is to show that these distributions are unique fixed…

We study preferential attachment mechanisms in random graphs that are parameterized by (i) a constant bias affecting the degree-biased distribution on the vertex set and (ii) the distribution of times at which new vertices are created by…

We prove a central limit theorem for a certain class of functions on sparse rank-one inhomogeneous random graphs endowed with additional i.i.d. edge and vertex weights. Our proof of the central limit theorem uses a perturbative form of…

We consider a variation on the Barab\'asi-Albert random graph process with fixed parameters $m\in \mathbb{N}$ and $1/2 < p < 1$. With probability $p$ a vertex is added along with $m$ edges, randomly chosen proportional to vertex degrees.…

A version of ``preferential attachment'' random graphs, corresponding to linear ``weights'' with random ``edge additions,'' which generalizes some previously considered models, is studied. This graph model is embedded in a continuous-time…

We study the number $X^{(n)}$ of vertices that can be reached from the last added vertex $n$ via a directed path (the descendants) in the standard preferential attachment graph. In this model, vertices are sequentially added, each born with…

We prove a central limit theorem for the components of the largest eigenvectors of the adjacency matrix of a finite-dimensional random dot product graph whose true latent positions are unknown. In particular, we follow the methodology…