is preferential attachment. Using data on co-authorship in economics, we estimate a model of preferential attachment with unobserved heterogeneity. Our main finding is that the evidence for preferential attachment evaporates once we control for individual heterogeneity in the propensity to form new links.

Abstract. Models based on preferential attachment have had much success in reproducing the power law degree distributions which seem ubiquitous in both natural and engineered systems. Here, rather than assuming preferential attachment, we give an explanation of how it can arise from a more basic

We consider the degree distributions of preferential attachment ran-dom graph models with choice similar to those considered in recent work by Malyshkin and Paquette and Krapivsky and Redner. In these models a new vertex chooses r vertices according to a preferential rule and connects to the vertex

We study empirically the time evolution of scientific collaboration networks in physics and biology. In these networks, two scientists are considered connected if they have coauthored one or more papers together. We show that the probability of scientists collaborating increases with the number of other collaborators they have in common, and that the probability of a particular scientist acquiring new collaborators increases with the number of his or her past collaborators. These results provide experimental evidence in favor of previously conjectured mechanisms for clustering and power-law degree distributions in networks. 1 I.

depending on their number of neighbours. Such models are called “preferential attachment models”. There are several variants of such models. In this project, we will consider some of the literature on such models, e.g. starting from Athreya et al., which is written in an accessible way for a student who has

In this paper, we investigate the diameter in preferential attachment (PA-) models, thus quantifying the statement that these models are small worlds. The models studied here are such that edges are attached to older vertices proportional to the degree plus a constant, i.e., we consider affine PA

. When a new node joins the network, it chooses neighbors according to preferential attachment, and then chooses its type based on the number of initial neighbors of each type. This can model a new cell-phone user choosing a cell-phone provider, a new student choosing a laptop, or a new athletic team

In this paper, we investigate the diameter in preferential attachment (PA-) models, thus quantifying the statement that these models are small worlds. There is a substantial amount of literature proving that, in quite generality, PA-graphs possess power-law degree sequences with exponent τ> 2

Abstract. 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 neighbors are sampled from the existing vertices

Abstract not found