Structural vector autoregressions allow contemporaneous series dependence and assume errors with no contemporaneous correlation. Models of this form, that also have a recursive structure, can be described by a directed acyclic graph.An important tool for identification of these models is the conditional independence graph constructed from the contemporaneous and lagged values of the process. We determine the large-sample properties of statistics used to test for the presence of links in this graph. A simple example illustrates how these results may be applied.