  With the aid of the concept of stable independence we can construct, in an
efficient way, a compact representation of a semi-graphoid independence
relation. We show that this representation provides a new necessary condition
for the existence of a directed perfect map for the relation. The test for this
condition is based to a large extent on the transitivity property of a special
form of d-separation. The complexity of the test is linear in the size of the
representation. The test, moreover, brings the additional benefit that it can
be used to guide the early stages of network construction.
