Asymptotic normality of degree counts in a preferential attachment model
نویسندگان
چکیده
منابع مشابه
Expected degree of finite preferential attachment networks
Abstract We provide an analytic expression for the quantity described in the title. Namely, we perform a preferential attachment growth process to generate a scale-free network. At each stage we add a new node with m new links. Let k denote the degree of a node, and N the number of nodes in the network. The degree distribution is assumed to converge to a power-law (for k ≥ m) of the form k and ...
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For the directed edge preferential attachment network growth model studied by Bollobás et al. (2003) and Krapivsky and Redner (2001), we prove that the joint distribution of in-degree and out-degree has jointly regularly varying tails. Typically the marginal tails of the in-degree distribution and the out-degree distribution have different regular variation indices and so the joint regular vari...
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Many empirically studied networks have approximately so-called power-law or scale-free degree distributions. In Section 1 we formally define such distributions and explore some of their properties. We also introduce and briefly compare two methods for constructing random networks with approximately power-law degree distributions: generic scale-free networks and the preferential attachment model...
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In their paper [1] Barabási and Albert proposed a certain random process of evolving graphs as a model of real-world networks, like the Internet. In their model vertices are added to the graph one by one, and edges connecting the new vertex to the old ones are drawn randomly, with probabilities proportional to the degree of the endpoint. In the particular case where only a single edge is allowe...
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We study a random graph Gn that combines certain aspects of geometric random graphs and preferential attachment graphs. The vertices of Gn are n sequentially generated points x1, x2, . . . , xn chosen uniformly at random from the unit sphere in R . After generating xt, we randomly connect it to m points from those points in x1, x2, . . . , xt−1 which are within distance r. Neighbors are chosen ...
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ژورنال
عنوان ژورنال: Advances in Applied Probability
سال: 2016
ISSN: 0001-8678,1475-6064
DOI: 10.1017/apr.2016.56