Related papers: PageRank Asymptotics on Directed Preferential Atta…
A variation of the preferential attachment random graph model of Barab\'asi and Albert is defined that incorporates planted communities. The graph is built progressively, with new vertices attaching to the existing ones one-by-one. At every…
Abel-Tauberian theorems relate power law behavior of distributions and their transforms. We formulate and prove a multivariate version for non-standard regularly varying measures on $\mathbb{R}_+^p$ and then apply it to prove that the joint…
We present an analysis of the statistical properties and growth of the free on-line encyclopedia Wikipedia. By describing topics by vertices and hyperlinks between them as edges, we can represent this encyclopedia as a directed graph. The…
A dynamic model for a random network evolving in continuous time is defined where new vertices are born and existing vertices may die. The fitness of a vertex is defined as the accumulated in-degree of the vertex and a new vertex is…
There are diverse mechanisms driving the evolution of social networks. A key open question dealing with understanding their evolution is: How various preferential linking mechanisms produce networks with different features? In this paper we…
A preferential attachment model for a growing network incorporating deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step $t=1,2,\ldots$, with probability $\pi_1>0$ a new vertex with one…
Understanding the structure and evolution of online bipartite networks is a significant task since they play a crucial role in various e-commerce services nowadays. Recently, various attempts have been tried to propose different models,…
We show that the load at each node in a preferential attachment network scales as a power of the degree of the node. For a network whose degree distribution is p(k) ~ k^(-gamma), we show that the load is l(k) ~ k^eta with eta = gamma - 1,…
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…
The "power of choice" has been shown to radically alter the behavior of a number of randomized algorithms. Here we explore the effects of choice on models of tree and network growth. In our models each new node has k randomly chosen…
Over the last few decades power law distributions have been suggested as forming generative mechanisms in a variety of disparate fields, such as, astrophysics, criminology and database curation. However, fitting these heavy tailed…
This paper analyzes key properties of networks generated by geometric preferential attachment. We establish that the expected number of triangles is proportional to that of the standard preferential attachment model, with a proportionality…
We consider a growing network, whose growth algorithm is based on the preferential attachment typical for scale-free constructions, but where the long-range bonds are disadvantaged. Thus, the probability to get connected to a site at…
Recently several authors have proposed stochastic evolutionary models for the growth of complex networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get…
We study an evolving spatial network in which sequentially arriving vertices are joined to existing vertices at random according to a rule that combines preference according to degree with preference according to spatial proximity. We…
We show that to explain the growth of the citation network by preferential attachment (PA), one has to accept that individual nodes exhibit heterogeneous fitness values that decay with time. While previous PA-based models assumed either…
Graph neural network (GNN) link prediction is increasingly deployed in citation, collaboration, and online social networks to recommend academic literature, collaborators, and friends. While prior research has investigated the dyadic…
We provide a local probabilistic description of the limiting statistics of large preferential attachment trees in terms of the ordinary degree (number of neighbors) but augmented with information on leafdegree (number of neighbors that are…
We introduce a model for directed spatial networks. Starting from an age-based preferential attachment model in which all arcs point from younger to older vertices, we add \emph{reciprocal} connections whose probabilities depend on the age…
Preferential attachment is a popular generative mechanism to explain the widespread observation of power law distributed networks. We introduce an alternative explanation for the phenomenon by allowing the link growth rates to vary across…