  For a directed acyclic graph, there are two known criteria to decide whether
any specific conditional independence statement is implied for all
distributions factorized according to the given graph. Both criteria are based
on special types of path in graphs. They are called separation criteria because
independence holds whenever the conditioning set is a separating set in a graph
theoretical sense. We introduce and discuss an alternative approach using
binary matrix representations of graphs in which zeros indicate independence
statements. A matrix condition is shown to give a new path criterion for
separation and to be equivalent to each of the previous two path criteria.
