No abstract

In this paper we present the application of a novel methodology to scientific citation and collaboration networks. This methodology is designed for understanding the governing dynamics of evolving networks and relies on an attachment kernel, a scalar function of node properties, which stochastically drives the addition and deletion of vertices and edges. We illustrate how the kernel function of a given network can be extracted from the history of the network and discuss other possible applications.

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.