  This paper is concerned with cross-sectional dependence arising because
observations are interconnected through an observed network. Following Doukhan
and Louhichi (1999), we measure the strength of dependence by covariances of
nonlinearly transformed variables. We provide a law of large numbers and
central limit theorem for network dependent variables. We also provide a method
of calculating standard errors robust to general forms of network dependence.
For that purpose, we rely on a network heteroskedasticity and autocorrelation
consistent (HAC) variance estimator, and show its consistency. The results rely
on conditions characterized by tradeoffs between the rate of decay of
dependence across a network and network's denseness. Our approach can
accommodate data generated by network formation models, random fields on
graphs, conditional dependency graphs, and large functional-causal systems of
equations.
