  In most studies, street networks are considered as undirected graphs while
one-way streets and their effect on shortest paths are usually ignored. Here,
we first study the empirical effect of one-way streets in about $140$ cities in
the world. Their presence induces a detour that persists over a wide range of
distances and characterized by a non-universal exponent. The effect of one-ways
on the pattern of shortest paths is then twofold: they mitigate local traffic
in certain areas but create bottlenecks elsewhere. This empirical study leads
naturally to consider a mixed graph model of 2d regular lattices with both
undirected links and a diluted variable fraction $p$ of randomly directed links
which mimics the presence of one-ways in a street network. We study the size of
the strongly connected component (SCC) versus $p$ and demonstrate the existence
of a threshold $p_c$ above which the SCC size is zero. We show numerically that
this transition is non-trivial for lattices with degree less than $4$ and
provide some analytical argument. We compute numerically the critical exponents
for this transition and confirm previous results showing that they define a new
universality class different from both the directed and standard percolation.
Finally, we show that the transition on real-world graphs can be understood
with random perturbations of regular lattices. The impact of one-ways on the
graph properties were already the subject of a few mathematical studies, and
our results show that this problem has also interesting connections with
percolation, a classical model in statistical physics.
