Related papers: Asymptotic Critical Radii in Random Geometric Grap…

This article presents the precise asymptotical distribution of two types of critical transmission radii, defined in terms of k-connectivity and the minimum vertex degree, for random geometry graphs distributed over three-dimensional…

This article presents the precise asymptotical distribution of two types of critical transmission radii, defined in terms of k-connectivity and the minimum vertex degree, for a random geometry graph distributed over a 3-Dimensional Convex…

We establish the asymptotic degree distribution of the typical vertex of inhomogeneous and passive random intersection graphs under the minimal moment conditions.

We analyse graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present. The critical connectivity is found numerically by examining the size…

Let $X_1,X_2,...$ be an infinite sequence of i.i.d. random vectors distributed exponentially with parameter $\lam .$ For each $y$ and $n\geq 1,$ form a graph $G_n(y)$ with vertex set $V_n = \{X_1,...,X_n\},$ two vertices are connected if…

We give an explicit construction of the weak local limit of a class of preferential attachment graphs. This limit contains all local information and allows several computations that are otherwise hard, for example, joint degree…

Let $G$ be a finite connected graph on two or more vertices and $G^{[N,k]}$ the distance $k$-graph of the $N$-fold Cartesian power of $G$. For a fixed $k\ge1$, we obtain explicitly the large $N$ limit of the spectral distribution (the…

We give quadratic upper bounds for the asymptotic dimensions of the arc graphs and disk graphs.

In several scale free graph models the asymptotic degree distribution and the characteristic exponent change when only a smaller set of vertices is considered. Looking at the common properties of these models, we present sufficient…

Topological indices play a significant role in mathematical chemistry. Given a graph $\mathcal{G}$ with vertex set $\mathcal{V}=\{1,2,\dots,n\}$ and edge set $\mathcal{E}$, let $d_i$ be the degree of node $i$. The degree-based topological…

The aim of this short article is to convey the basic idea of the original paper [3], without going into too much detail, about how to derive sharp asymptotics of the gyration radius for random walk, self-avoiding walk and oriented…

In this paper we study the one dimensional random geometric graph when the location of the nodes are independent and exponentially distributed. We derive exact results and the limit theorems for the connectivity and other properties…

In this work we give precise asymptotic expressions on the probability of the existence of fixed-size components at the threshold of connectivity for random geometric graphs.

In this work we introduce Dynamic Random Geometric Graphs as a basic rough model for mobile wireless sensor networks, where communication distances are set to the known threshold for connectivity of static random geometric graphs. We…

We show the asymptotic degree distribution of the typical vertex of a sparse inhomogeneous random intersection graph.

We deal with a general preferential attachment graph model with multiple type edges. The types are chosen randomly, in a way that depends on the evolution of the graph. In the $N$-type case, we define the (generalized) degree of a given…

We consider a variant of so called power-law random graph. A sequence of expected degrees corresponds to a power-law degree distribution with finite mean and infinite variance. In previous works the asymptotic picture with number of nodes…

We study the asymptotic distribution, as the volume parameter goes to 1, of the peak (largest part) of finite- or slowly-growing-width cylindric plane partitions weighted by their trace, seam, and volume. There are two natural asymptotic…

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…

The study of random surfaces, especially in the asymptotics of large genus, has been of increasing interest in recent years. Many geometrical questions have analogous formulations in the theory of random graphs with a large number of…