Related papers: Analytic solution for preferential attachment prob…
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…
Discovery problems often require deciding whether additional sampling is needed to detect all categories whose prevalence exceeds a prespecified threshold. We study this question under a Bernoulli product (incidence) model, where categories…
We consider a preferential attachment process in which a multigraph is built one node at a time. The number of edges added at stage $t$, emanating from the new node, is given by some prescribed function $f(t)$, generalising a model…
In this paper, we characterise the notion of preferential attachment in networks as action at a distance, and argue that it can only be an emergent phenomenon -- the actual mechanism by which networks grow always being the closing of…
Relevance and importance are the main factors when humans build network connections. We propose an evolutionary network model based on preferential attachment(PA) considering these factors. We analyze and compute several important features…
We introduce quantum association schemes. This allows to define distance regular and strongly regular quantum graphs. We bring examples thereof. In addition, we formulate the duality for translation quantum association schemes corresponding…
The aim of this paper is to study a dimorphic property associated with two different sums of identically independent Bernoulli random variables having two different families of probability mass functions. In addition, we give two…
It is commonly believed that real networks are scale-free and fraction of nodes $P(k)$ with degree $k$ satisfies the power law $P(k) \propto k^{-\gamma} \text{ for } k > k_{min} > 0$. Preferential attachment is the mechanism that has been…
The hidden variable formalism (based on the assumption of some intrinsic node parameters) turned out to be a remarkably efficient and powerful approach in describing and analyzing the topology of complex networks. Owing to one of its most…
Presence/absence data and presence-only data are the two customary sources for learning about species distributions over a region. We illuminate the fundamental modeling differences between the two types of data. Most simply, locations are…
We discuss a new stochastic ordering for the sequence of independent random variables. It generalizes the stochastic precedence order that is defined for two random variables to the case $n>2$. All conventional stochastic orders are…
In order to better understand dynamical functions on amounts of natural and man-made complex systems, lots of researchers from a wide range of disciplines, covering statistic physics, mathematics, theoretical computer science, and so on,…
Scale independence is a ubiquitous feature of complex systems which implies a highly skewed distribution of resources with no characteristic scale. Research has long focused on why systems as varied as protein networks, evolution and stock…
We consider $N$ Bernoulli random variables, which are independent conditional on a common random factor determining their probability distribution. We show that certain expected functionals of the proportion $L_N$ of variables in a given…
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 consider the use of random walks as an approach to obtain connection coefficients for higher-order Bernoulli and Euler polynomials. In particular, we consider the cases of a $1$-dimensional linear reflected Brownian motion and of a…
We consider a preferential attachment model that incorporates an anomaly. Our goal is to understand the evolution of the network before and after the occurrence of the anomaly by studying the influence of the anomaly on the structural…
Suppose in a graph $G$ vertices can be either red or blue. Let $k$ be odd. At each time step, each vertex $v$ in $G$ polls $k$ random neighbours and takes the majority colour. If it doesn't have $k$ neighbours, it simply polls all of them,…
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…
The paper deals with three generalized dependent setups arising from a sequence of Bernoulli trials. Various distributional properties, such as probability generating function, probability mass function and moments are discussed for these…