A detailed understanding of expansion in complex networks can greatly aid in the design and analysis of algorithms for a variety of important network tasks, including routing messages, ranking nodes, and compressing graphs. This has motivated several recent investigations of expansion properties in real-world graphs and also in random models of real-world graphs, like the preferential attachment graph. The results point to a gap between real-world observations and theoretical models. Some real-world graphs are expanders and others are not, but a graph generated by the preferential attachment model is an expander whp.#R##N##R##N#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.#R##N##R##N#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 in x1, x2, ..., xt-1....
['Abraham D. Flaxman', 'Alan M. Frieze', 'Juan Carlos Vera']
A geometric preferential attachment model of networks II