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Complex networks characterized by global transport processes rely on thepresence of directed paths from input to output nodes and edges, which organizein characteristic linked components. The analysis of such network-spanningstructures in the framework of percolation theory, and in particular the keyrole of edge interfaces bridging the communication between core and periphery,allow us to shed light on the structural properties of real and theoreticalflow networks, and to define criteria and quantities to characterize theirefficiency at the interplay between structure and functionality. In particular,it is possible to assess that an optimal flow network should look like a "hairyball", so to minimize bottleneck effects and the sensitivity to failures.Moreover, the thorough analysis of two real networks, the Internetcustomer-provider set of relationships at the autonomous system level and thenervous system of the worm Caenorhabditis elegans --that have been shaped byvery different dynamics and in very different time-scales--, reveals thatwhereas biological evolution has selected a structure close to the optimallayout, market competition does not necessarily tend toward the most customerefficient architecture.

Structural efficiency of percolation landscapes in flow networks