Related papers: A counter-example to persistence in generalised pr…
We prove almost sure convergence of the maximum degree in an evolving tree model combining local choice and preferential attachment. At each step in the growth of the graph, a new vertex is introduced. A fixed, finite number of possible…
A vertex of a randomly growing graph is called a persistent hub if at all but finitely many moments of time it has the maximal degree in the graph. We establish the existence of a persistent hub in the Barab\'asi--Albert random graph model…
We consider models of evolving networks $\{\mathcal{G}_n:n\geq 0\}$ modulated by two parameters: an attachment function $f:\mathbb{N}_0\to\mathbb{R}_+$ and a (possibly random) attachment sequence $\{m_i:i\geq 1\}$. Starting with a single…
We propose an empirical estimator of the preferential attachment function $f$ in the setting of general preferential attachment trees. Using a supercritical continuous-time branching process framework, we prove the almost sure consistency…
A sequence of trees $(\mathcal{T}_{n})_{n \in \mathbb{N}}$ contains a \emph{persistent hub}, or displays \emph{degree centrality}, if there is a fixed node of maximal degree for all sufficiently large $n \in \mathbb{N}$. We derive…
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…
We investigate properties of node centrality in random growing tree models. We focus on a measure of centrality that computes the maximum subtree size of the tree rooted at each node, with the most central node being the tree centroid. For…
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 consider a preferential attachment random graph with self-reinforcement. Each time a new vertex comes in, it attaches itself to an old vertex with a probability that is proportional to the sum of the degrees of that old vertex at all…
We consider an evolving random discrete tree model called Preferential Attachment with Vertex Death, as introduced by Deijfen. Initialised with an alive root labelled $1$, at each step $n\geq1$ either a new vertex with label $n+1$ is…
We find assimpotics for the first $k$ highest degrees of the degree distribution in an evolving tree model combining the local choice and the preferential attachment. In the considered model, the random graph is constructd in the following…
In this work we consider a growing random graph sequence where a new vertex is less likely to join to an existing vertex with high degree and more likely to join to a vertex with low degree. In contrast to the well studied…
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…
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 the preferential attachment model. This is a growing random graph such that at each step a new vertex is added and forms $m$ connections. The neighbors of the new vertex are chosen at random with probability proportional to…
We consider a general preferential attachment model, where the probability that a newly arriving vertex connects to an older vertex is proportional to a sublinear function of the indegree of the older vertex at that time. It is well known…
We study a new class of preferential attachment trees with \emph{self-reinforcement}. At each time, each vertex is assigned a weight equal to the cumulative sum over past times of an affine function of its degree. A new vertex attaches…
We introduce a model of a preferential attachment based random graph which extends the family of models in which condensation phenomena can occur. Each vertex has an associated uniform random variable which we call its location. Our model…
We study preferential attachment models where vertices enter the network with i.i.d. random numbers of edges that we call the out-degree. We identify the local limit of such models, substantially extending the work of Berger et al.(2014).…
A version of ``preferential attachment'' random graphs, corresponding to linear ``weights'' with random ``edge additions,'' which generalizes some previously considered models, is studied. This graph model is embedded in a continuous-time…