  We propose an information-theoretic framework to quantify multipartite
correlations in classical and quantum systems, answering questions such as:
what is the amount of seven-partite correlations in a given state of ten
particles? We identify measures of genuine multipartite correlations, i.e.
statistical dependencies which cannot be ascribed to bipartite correlations,
satisfying a set of desirable properties. Inspired by ideas developed in
complexity science, we then introduce the concept of weaving to classify states
which display different correlation patterns, but cannot be distinguished by
correlation measures. The weaving of a state is defined as the weighted sum of
correlations of every order. Weaving measures are good descriptors of the
complexity of correlation structures in multipartite systems.
