Abstract
We investigate the asymptotic properties of a random tree growth model which generalizes the basic concept of preferential attachment. The Barabási-Albert random graph model is based on the idea that the popularity of a vertex in the graph (the probability that a new vertex will be attached to it) is proportional to its current degree. The dependency on the degree, the so-called weight function, is linear in this model. We give results which are valid for a much wider class of weight functions. This generalized model has been introduced by Krapivsky and Redner in the physics literature. The method of re-phrasing the model in a continuous-time setting makes it possible to connect the problem to the welldeveloped theory of branching processes. We give local results, concerning the neighborhood of a “typical” vertex in the tree, and also global ones, about the repartition of mass between subtrees under fixed vertices.
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© 2008 János Bolyai Mathematical Society and Springer-Verlag
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Rudas, A., Tóth, B. (2008). Random Tree Growth with Branching Processes — A Survey. In: Bollobás, B., Kozma, R., Miklós, D. (eds) Handbook of Large-Scale Random Networks. Bolyai Society Mathematical Studies, vol 18. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69395-6_4
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DOI: https://doi.org/10.1007/978-3-540-69395-6_4
Publisher Name: Springer, Berlin, Heidelberg
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