Related papers: The Yule distribution and frailty--a note on spuri…
Many complex natural and physical systems exhibit patterns of interconnection that conform, approximately, to a network structure referred to as scale-free. Preferential attachment is one of many algorithms that have been introduced to…
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…
We study a generalization of the affine preferential attachment model where triangles are randomly added to the graph. We show that the model exhibits an asymptotically power-law degree distribution with adjustable parameter $\gamma\in…
We study a model for the evolution of chemical species under a combination of population dynamics on a short time scale and a selection mechanism on a longer time scale. Least fit nodes are replaced by new nodes whose links are attached to…
Network science is a powerful framework allowing to model complex systems, it is capable to describe and take into account the intricate web of connections existing among the constituting basic element of the system. Recently scholars have…
We present analytical results for the effect of preferential node deletion on the structure of networks that evolve via node addition and preferential attachment. To this end, we consider a preferential-attachment-preferential-deletion…
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 characterize the tail behavior of the distribution of the PageRank of a uniformly chosen vertex in a directed preferential attachment graph and show that it decays as a power law with an explicit exponent that is described in terms of…
Preferential attachment probabilities scheme appear in the context of scale free random graphs [1],[2]. In this work we present preferential attachment probabilities scheme as a sequence of dependent Bernoulli random variables and we give…
Leaves, i.e., vertices of degree one, can play a significant role in graph structure, especially in sparsely connected settings in which leaves often constitute the largest fraction of vertices. We consider a leaf-based counterpart of the…
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…
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…
It appeared recently that the underlying degree distribution of networks may play a crucial role concerning their robustness. Empiric and analytic results have been obtained, based on asymptotic and mean-field approximations. Previous work…
Efforts to reconstruct phylogenetic trees and understand evolutionary processes depend fundamentally on stochastic models of speciation and mutation. The simplest continuous-time model for speciation in phylogenetic trees is the Yule…
We propose a random graph model with preferential attachment rule and \emph{edge-step functions} that govern the growth rate of the vertex set. We study the effect of these functions on the empirical degree distribution of these random…
We consider the preferential attachment model with location-based choice introduced by Haslegrave, Jordan and Yarrow as a model in which condensation phenomena can occur [Haslegrave et al. 2020]. In this model every vertex carries an…
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…
We prove almost sure convergence of the maximum degree in an evolving graph model combining a growing number of local choices with sublinear preferential attachment. At each step in the growth of the graph, a new vertex is introduced. Then…
We investigate a growing network model that combines preferential and uniform attachment with two distinct mechanisms of edge deletion. In addition to the usual uniform probability edge deletion, we introduce a novel node-based rule in…
Simple growth mechanisms have been proposed to explain the emergence of seemingly universal network structures. The widely-studied model of preferential attachment assumes that new nodes are more likely to connect to highly connected nodes.…