相关论文: Degrees in random $m$-ary hooking networks

The degree distributions of complex networks are usually considered to be power law. However, it is not the case for a large number of them. We thus propose a new model able to build random growing networks with (almost) any wanted degree…

In this paper, we consider a one-dimensional random geometric graph process with the inter-nodal gaps evolving according to an exponential AR(1) process, which may serve as a mobile wireless network model. The transition probability matrix…

In this paper, we investigate the exact asymptotic behavior of the connectivity probability in the Erdos-Renyi graph G(n,p), under different asymptotic assumptions on the edge probability p=p(n). We propose a novel approach based on the…

We count the asymptotic number of triangles in uniform random graphs where the degree distribution follows a power law with degree exponent $\tau\in(2,3)$. We also analyze the local clustering coefficient $c(k)$, the probability that two…

We study the problem of generating connected random graphs with no self-loops or multiple edges and that, in addition, have a given degree sequence. The generation method we focus on is the edge-switching Markov-chain method, whose…

A random geometric digraph $G_n$ is constructed by taking $\{X_1,X_2,... X_n\}$ in $\mathbb{R}^2$ independently at random with a common bounded density function. Each vertex $X_i$ is assigned at random a sector $S_i$ of central angle…

The ever increasing availability of data demands for techniques to extract relevant information from complex interacting systems, which can often be represented as weighted networks. In recent years, a number of approaches have been…

We discuss several limiting degree distributions for a class of random threshold graphs in the many node regime. This analysis is carried out under a weak assumption on the distribution of the underlying fitness variable. This assumption,…

Generalized P\'olya urns with non-linear feedback are an established probabilistic model to describe the dynamics of growth processes with reinforcement, a generic example being competition of agents in evolving markets. It is well known…

In complex networks the degrees of adjacent nodes may often appear dependent -- which presents a modelling challenge. We present a working framework for studying networks with an arbitrary joint distribution for the degrees of adjacent…

Motivated by low energy consumption in geographic routing in wireless networks, there has been recent interest in determining bounds on the length of edges in the Delaunay graph of randomly distributed points. Asymptotic results are known…

Large real-life complex networks are often modeled by various random graph constructions and hundreds of further references therein. In many cases it is not at all clear how the modeling strength of differently generated random graph model…

Tree shape statistics provide valuable quantitative insights into evolutionary mechanisms underpinning phylogenetic trees, a commonly used graph representation of evolution systems ranging from viruses to species. By developing limit…

Consider a network of agents that all want to guess the correct value of some ground truth state. In a sequential order, each agent makes its decision using a single private signal which has a constant probability of error, as well as…

A P\'olya urn process is a Markov chain that models the evolution of an urn containing some coloured balls, the set of possible colours being $\{1,\ldots,d\}$ for $d\in \mathbb{N}$. At each time step, a random ball is chosen uniformly in…

A P\'olya urn of replacement matrix $R=(R_{i,j})_{1\leq i,j\leq d}$ is a Markov process that encodes the following experiment: an urn contains balls of $d$ different colours and at every time-step, a ball is drawn uniformly at random in the…

We consider limit probabilities of first order properties in random graphs with a given degree sequence. Under mild conditions on the degree sequence, we show that the closure set of limit probabilities is a finite union of closed…

We study the random graph G_{n,\lambda/n} conditioned on the event that all vertex degrees lie in some given subset S of the non-negative integers. Subject to a certain hypothesis on S, the empirical distribution of the vertex degrees is…

Graph symmetries intervene in diverse applications, from enumeration, to graph structure compression, to the discovery of graph dynamics (e.g., node arrival order inference). Whereas Erd\H{o}s-R\'enyi graphs are typically asymmetric, real…

In this paper we introduce the perturbed version of the Barab\'asi-Albert random graph with multiple type edges and prove the existence of the (generalized) asymptotic degree distribution. Similarly to the non-perturbed case, the asymptotic…