  We investigate a class of growing graphs embedded into the $d$-dimensional
torus where new vertices arrive according to a Poisson process in time, are
randomly placed in space and connect to existing vertices with a probability
depending on time, their spatial distance and their relative ages. This simple
model for a scale-free network is called the age-based spatial preferential
attachment network and is based on the idea of preferential attachment with
spatially induced clustering. We show that the graphs converge weakly locally
to a variant of the random connection model, which we call the age-dependent
random connection model. This is a natural infinite graph on a Poisson point
process where points are marked by a uniformly distributed age and connected
with a probability depending on their spatial distance and both ages. We use
the limiting structure to investigate asymptotic degree distribution,
clustering coefficients and typical edge lengths in the age-based spatial
preferential attachment network.
