  This paper develops new limit theory for data that are generated by networks
or more generally display cross-sectional dependence structures that are
governed by observable and unobservable characteristics. Strategic network
formation models are an example. Wether two data points are highly correlated
or not depends on draws from underlying characteristics distributions. The
paper defines a measure of closeness that depends on primitive conditions on
the distribution of observable characteristics as well as functional form of
the underlying model. A summability condition over the probability distribution
of observable characteristics is shown to be a critical ingredient in
establishing limit results. The paper establishes weak and strong laws of large
numbers as well as a stable central limit theorem for a class of statistics
that include as special cases network statistics such as average node degrees
or average peer characteristics. Some worked examples illustrating the theory
are provided.
