  A characterization of the complete correlation structure in an $n$-party
system is proposed in terms of a series of $(k,n)$ threshold classical secret
sharing protocols ($2\le k\le n$). The total correlation is shown to be the sum
of independent correlations of 2-, 3-,$...$, $n$-parties. Our result unifies
several earlier scattered works, and shines new light at the important topic of
multi-party quantum entanglement. As an application, we explicitly construct
the hierarchy of correlations in an $n$-qubit graph state.
