  The covariance graph (aka bi-directed graph) of a probability distribution
$p$ is the undirected graph $G$ where two nodes are adjacent iff their
corresponding random variables are marginally dependent in $p$. In this paper,
we present a graphical criterion for reading dependencies from $G$, under the
assumption that $p$ satisfies the graphoid properties as well as weak
transitivity and composition. We prove that the graphical criterion is sound
and complete in certain sense. We argue that our assumptions are not too
restrictive. For instance, all the regular Gaussian probability distributions
satisfy them.
