A Geometric Preferential Attachment Model of Networks II

Abstract

We study a random graph $G_n$ 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 $G_n$ are $n$ sequentially generated points, $x_1,x_2,\ldots,x_n$, chosen uniformly at random from the unit sphere in R$^3$. After generating $x_t$, we randomly connect it to $m$ points from those points $x_1,x_2,\ldots,x_{t-1}$.