Multivariate entropy analysis of network data

Multigraphs with numerical or qualitative attributes defined on vertices and edges can benefit from systematic methods based on multivariate entropies for describing and analysing the interdependencies that are present between vertex and edge attributes. This is here illustrated by application of these tools to a subset of data on the social relations among Renaissance Florentine families collected by John Padgett. Using multivariate entropies we show how it is possible to systematically check for tendencies in data that can be described as independencies or conditional independencies, or as dependencies allowing certain combinations of variables to predict other variables. We also show how different structural models can be tested by divergence measures obtained from the multivariate entropies.