  This paper reports results of a network theory approach to the study of the
United States patent system. We model the patent citation network as a discrete
time, discrete space stochastic dynamic system. From data on more than 2
million patents and their citations, we extract an attractiveness function,
$A(k,l)$, which determines the likelihood that a patent will be cited. $A(k,l)$
is approximately separable into a product of a function $A_k(k)$ and a function
$A_l(l)$, where $k$ is the number of citations already received (in-degree) and
$l$ is the age measured in patent number units. $A_l(l)$ displays a peak at low
$l$ and a long power law tail, suggesting that some patented technologies have
very long-term effects. $A_k(k)$ exhibits super-linear preferential attachment.
The preferential attachment exponent has been increasing since 1991, suggesting
that patent citations are increasingly concentrated on a relatively small
number of patents. The overall average probability that a new patent will be
cited by a given patent has increased slightly during the same period. We
discuss some possible implications of our results for patent policy.
