  We show that abrupt structural transitions can arise in functionally optimal
networks, driven by small changes in the level of transport congestion. Our
results offer an explanation as to why so many diverse species of network
structure arise in Nature (e.g. fungal systems) under essentially the same
environmental conditions. Our findings are based on an exactly solvable model
system which mimics a variety of biological and social networks. We then extend
our analysis by introducing a novel renormalization scheme involving cost
motifs, to describe analytically the average shortest path across
multiple-ring-and-hub networks. As a consequence, we uncover a 'skin effect'
whereby the structure of the inner multi-ring core can cease to play any role
in terms of determining the average shortest path across the network.
