  Complex networks characterized by global transport processes rely on the
presence of directed paths from input to output nodes and edges, which organize
in characteristic linked components. The analysis of such network-spanning
structures in the framework of percolation theory, and in particular the key
role of edge interfaces bridging the communication between core and periphery,
allow us to shed light on the structural properties of real and theoretical
flow networks, and to define criteria and quantities to characterize their
efficiency at the interplay between structure and functionality. In particular,
it is possible to assess that an optimal flow network should look like a "hairy
ball", so to minimize bottleneck effects and the sensitivity to failures.
Moreover, the thorough analysis of two real networks, the Internet
customer-provider set of relationships at the autonomous system level and the
nervous system of the worm Caenorhabditis elegans --that have been shaped by
very different dynamics and in very different time-scales--, reveals that
whereas biological evolution has selected a structure close to the optimal
layout, market competition does not necessarily tend toward the most customer
efficient architecture.
