Growth of preferential attachment random graphs via continuous-time branching processes
Probability
2007-05-23 v1
Abstract
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 branching scheme and, using the branching process apparatus, several results on the graph model asymptotics are obtained, some extending previous results, such as growth rates for a typical degree and the maximal degree, behavior of the vertex where the maximal degree is attained, and a law of large numbers for the empirical distribution of degrees which shows certain ``scale-free'' or ``power-law'' behaviors.
Cite
@article{arxiv.math/0701649,
title = {Growth of preferential attachment random graphs via continuous-time branching processes},
author = {K. B. Athreya and A. P. Ghosh and S. Sethuraman},
journal= {arXiv preprint arXiv:math/0701649},
year = {2007}
}
Comments
20 pages