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 R 3. After generating xt, we randomly connect it to m points from those points in x1, x2,..., xt−1. 1

Citations