measures for a DAG (directed acyclic graph)?
There are loads of measures of nodes in a DAG you could use.  For example:


How much the removal of node $v$ reduces the max flow from sources to sinks
the betweenness centrality of $v$
the in-degree of $v$ times the out-degree of $v$


The question should not be if there is a measure, but rather which measure is most appropriate.  That depends on the problem you're trying to solve.