Related papers: Weighted distances in scale-free preferential atta…
We use the framework of multivariate regular variation to analyse the extremal behaviour of preferential attachment models. To this end, we follow a directed linear preferential attachment model for a random, heavy-tailed number of steps in…
We introduce a family of one-dimensional geometric growth models, constructed iteratively by locally optimizing the tradeoffs between two competing metrics, and show that this family is equivalent to a family of preferential attachment…
Probability density function estimation with weighted samples is the main foundation of all adaptive importance sampling algorithms. Classically, a target distribution is approximated either by a non-parametric model or within a parametric…
There is a complex relation between the mechanism of preferential attachment, scale-free degree distributions and hyperbolicity in complex networks. In fact, both preferential attachment and hidden hyperbolic spaces often generate…
In the recent past, there has been a concerted effort to develop mathematical models for real-world networks and to analyze various dynamics on these models. One particular problem of significant importance is to understand the effect of…
Two kinds of evolving trees are considered here: the exponential trees, where subsequent nodes are linked to old nodes without any preference, and the Barab\'asi--Albert scale-free networks, where the probability of linking to a node is…
In this article we presented a brief study of the main network models with growth and preferential attachment. Such models are interesting because they present several characteristics of real systems. We started with the classical model…
A uniform recursive tree on $n$ vertices is a random tree where each possible $(n-1)!$ labeled recursive rooted tree is selected with equal probability. In this paper we introduce and study weighted trees, a non-uniform recursive tree model…
In this paper Raptor code ensembles with linear random precodes in a fixed-rate setting are considered. An expression for the average distance spectrum is derived and this expression is used to obtain the asymptotic exponent of the weight…
The statistics and machine learning communities have recently seen a growing interest in classification-based approaches to two-sample testing. The outcome of a classification-based two-sample test remains a rejection decision, which is not…
We investigate the weighted scale-free percolation (SFPW) model on $\mathbb Z^d$. In the SFPW model, the vertices of $\mathbb Z^d$ are assigned i.i.d. weights $(W_x)_{x\in \mathbb Z^d}$, following a power-law distribution with tail exponent…
Preferential attachment is often suggested to be the underlying mechanism of the growth of a network, largely due to that many real networks are, to a certain extent, scale-free. However, such attribution is usually made under debatable…
We investigate a network model based on an infinite regular square lattice embedded in the Euclidean plane where the node connection probability is given by the geometrical distance of nodes. We show that the degree distribution in the…
We study first passage percolation on the configuration model (CM) having power-law degrees with exponent $\tau\in [1,2)$. To this end we equip the edges with exponential weights. We derive the distributional limit of the minimal weight of…
We study the joint degree counts in proportional attachment random graphs and find a simple representation for the limit distribution in infinite sequence space. We show weak convergence with respect to the p-norm topology for appropriate p…
In this paper, we analyze assortativity of preferential attachment models. We deal with a wide class of preferential attachment models (PA-class). It was previously shown that the degree distribution in all models of the PA-class follows a…
We investigate the joint distribution of nodes of small degrees and the degree profile in preferential dynamic attachment circuits. In particular, we study the joint asymptotic distribution of the number of the nodes of outdegree $0$…
We investigate critical behaviors of a social contagion model on weighted networks. An edge-weight compartmental approach is applied to analyze the weighted social contagion on strongly heterogenous networks with skewed degree and weight…
In this paper, we study some important statistics of the random graph in the directed preferential attachment model introduced by B. Bollob\'as, C. Borgs, J. Chayes and O. Riordan. First, we find a new asymptotic formula for the expectation…
We consider a Gibbs distribution over all spanning trees of an undirected, edge weighted finite graph, where, up to normalization, the probability of each tree is given by the product of its edge weights. Defining the weighted degree of a…