Related papers: Preferential Attachment and Vertex Arrival Times
In this paper we investigate geometric properties of graphs generated by a preferential attachment random graph model with edge-steps. More precisely, at each time $t\in\mathbb{N}$, with probability $p$ a new vertex is added to the graph (a…
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…
A message passing algorithm is derived for recovering communities within a graph generated by a variation of the Barab\'{a}si-Albert preferential attachment model. The estimator is assumed to know the arrival times, or order of attachment,…
We introduce a model for a growing random graph based on simultaneous reproduction of the vertices. The model can be thought of as a generalisation of the reproducing graphs of Southwell and Cannings and Bonato et al to allow for a random…
In this paper, we first discuss the origin of preferential attachment. Then we establish the generalized preferential attachment which has two new properties; first, it encapsulates both the topological and weight aspects of a network,…
We study the growth of two competing infection types on graphs generated by the configuration model with a given degree sequence. Starting from two vertices chosen uniformly at random, the infection types spread via the edges in the graph…
We investigate the degree sequences of geometric preferential attachment graphs in general compact metric spaces. We show that, under certain conditions on the attractiveness function, the behaviour of the degree sequence is similar to that…
A random graph evolution based on the interactions of N vertices is studied. During the evolution both the preferential attachment method and the uniform choice of vertices are allowed. The weight of a vertex means the number of its…
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 study the following preferential attachment variant of the classical Erdos-Renyi random graph process. Starting with an empty graph on n vertices, new edges are added one-by-one, and each time an edge is chosen with probability roughly…
In this paper we focus on the problem of the degree sequence for the following random graph process. At any time-step $t$, one of the following three substeps is executed: with probability $\alpha_1$, a new vertex $x_t$ and $m$ edges…
We deal with a random graph model where at each step, a vertex is chosen uniformly at random, and it is either duplicated or its edges are deleted. Duplication has a given probability. We analyse the limit distribution of the degree of a…
We investigate the degree distribution resulting from graph generation models based on rank-based attachment. In rank-based attachment, all vertices are ranked according to a ranking scheme. The link probability of a given vertex is…
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…
We consider a variation on the Barab\'asi-Albert random graph process with fixed parameters $m\in \mathbb{N}$ and $1/2 < p < 1$. With probability $p$ a vertex is added along with $m$ edges, randomly chosen proportional to vertex degrees.…
We obtain closed form expressions for the expected conditional degree distribution and the joint degree distribution of the linear preferential attachment model for network growth in the steady state. We consider the multiple-destination…
This paper presents the development of a new class of algorithms that accurately implement the preferential attachment mechanism of the Barab\'asi-Albert (BA) model to generate scale-free graphs. Contrary to existing approximate…
We study the basic preferential attachment process, which generates a sequence of random trees, each obtained from the previous one by introducing a new vertex and joining it to one existing vertex, chosen with probability proportional to…
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…
We live in a world increasingly dominated by networks -- communications, social, information, biological etc. A central attribute of many of these networks is that they are dynamic, that is, they exhibit structural changes over time. While…