Is there a way to tweak the existing connected components algorithms (WCC & SCC) to compute unilaterally connected components?

The difference between each of them can be seen here:

Is there a way to tweak the existing connected components algorithms (WCC & SCC) to compute unilaterally connected components?

The difference between each of them can be seen here:

Nice question. Maybe just look and see if there is a spanning tree that is directed (i.e. , directed away from a single vertex)?