  We consider graphs that represent pairwise marginal independencies amongst a
set of variables (for instance, the zero entries of a covariance matrix for
normal data). We characterize the directed acyclic graphs (DAGs) that
faithfully explain a given set of independencies, and derive algorithms to
efficiently enumerate such structures. Our results map out the space of
faithful causal models for a given set of pairwise marginal independence
relations. This allows us to show the extent to which causal inference is
possible without using conditional independence tests.
