Abstract
We study a random graph _G_<sub> <em>n</em> </sub> 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_<sub> <em>n</em> </sub> are _n_ sequentially generated points, _x_<sub>1</sub>, _x_<sub>2</sub>, . . . , _x_<sub> <em>n</em> </sub>, chosen uniformly at random from the unit sphere in R<sup>3</sup> After generating _x_<sub> <em>t</em> </sub>, we randomly connect it to _m_ points from those points _x_<sub>1</sub>, _x_<sub>2</sub>, . . . , _x_<sub> <em>t</em>−1</sub>.
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