  We address the practical problems of estimating the information relations
that characterize large networks. Building on methods developed for analysis of
the neural code, we show that reliable estimates of mutual information can be
obtained with manageable computational effort. The same methods allow
estimation of higher order, multi--information terms. These ideas are
illustrated by analyses of gene expression, financial markets, and consumer
preferences. In each case, information theoretic measures correlate with
independent, intuitive measures of the underlying structures in the system.
