  We study property testing in directed graphs in the bounded degree model,
where we assume that an algorithm may only query the outgoing edges of a
vertex, a model proposed by Bender and Ron in 2002. As our first main result,
we we present a property testing algorithm for strong connectivity in this
model, having a query complexity of $\mathcal{O}(n^{1-\epsilon/(3+\alpha)})$
for arbitrary $\alpha>0$; it is based on a reduction to estimating the vertex
indegree distribution. For subgraph-freeness we give a property testing
algorithm with a query complexity of $\mathcal{O}(n^{1-1/k})$, where $k$ is the
number of connected componentes in the queried subgraph which have no incoming
edge. We furthermore take a look at the problem of testing whether a weakly
connected graph contains vertices with a degree of least $3$, which can be
viewed as testing for freeness of all orientations of $3$-stars; as our second
main result, we show that this property can be tested with a query complexity
of $\mathcal{O}(\sqrt{n})$ instead of, what would be expected,
$\Omega(n^{2/3})$.
