  Graphical models are a key class of probabilistic models for studying the
conditional independence structure of a set of random variables. Circular
variables are special variables, characterized by periodicity, arising in
several contexts and fields. However, models for studying the
dependence/independence structure of circular variables are under-explored.
This paper analyses three multivariate circular distributions, the von Mises,
the Wrapped Normal and the Inverse Stereographic distributions, focusing on
their properties concerning conditional independence. For each one of these
distributions, we discuss the main properties related to conditional
independence and introduce suitable classes of graphical models. The usefulness
of the proposed models is shown by modelling the conditional independence among
dihedral angles characterizing the three-dimensional structure of some
proteins.
