A geometric preferential attachment model of networks II

Abstract

We study a random graph Gn that combines certain aspects of geometric random graphs and preferential attachment graphs. This model yields a graph with power law degree distribution where the expansion property depends on a tunable parameter of the model. The vertices of Gn are n sequentially generated points, x1, x2,…, xn, chosen uniformly at random from the unit sphere in R3 After generating xt, we randomly connect it to m points from those points x1, x2,…, xt−1.