  Entropy and information provide natural measures of correlation among
elements in a network. We construct here the information theoretic analog of
connected correlation functions: irreducible $N$--point correlation is measured
by a decrease in entropy for the joint distribution of $N$ variables relative
to the maximum entropy allowed by all the observed $N-1$ variable
distributions. We calculate the ``connected information'' terms for several
examples, and show that it also enables the decomposition of the information
that is carried by a population of elements about an outside source.
