  We define a class of growing networks in which new nodes are given a spatial
position and are connected to existing nodes with a probability mechanism
favoring short distances and high degrees. The competition of preferential
attachment and spatial clustering gives this model a range of interesting
properties. Empirical degree distributions converge to a limit law, which can
be a power law with any exponent $\tau>2$. The average clustering coefficient
of the networks converges to a positive limit. Finally, a phase transition
occurs in the global clustering coefficients and empirical distribution of edge
lengths when the power-law exponent crosses the critical value $\tau=3$. Our
main tool in the proof of these results is a general weak law of large numbers
in the spirit of Penrose and Yukich.
