  The traditional node percolation map of directed networks is reanalyzed in
terms of edges. In the percolated phase, edges can mainly organize into five
distinct giant connected components, interfaces bridging the communication of
nodes in the strongly connected component and those in the in- and
out-components. Formal equations for the relative sizes in number of edges of
these giant structures are derived for arbitrary joint degree distributions in
the presence of local and two-point correlations. The uncorrelated null model
is fully solved analytically and compared against simulations, finding an
excellent agreement between the theoretical predictions and the edge
percolation map of synthetically generated networks with exponential or
scale-free in-degree distribution and exponential out-degree distribution.
Interfaces, and their internal organization giving place from "hairy ball"
percolation landscapes to bottleneck straits, could bring new light to the
discussion of how structure is interwoven with functionality, in particular in
flow networks.
