Interplay between function and structure in complex networks

Details Interplay between function and structure in complex networks Interplay between function and structure in complex networks

2006-04-21

arxiv.org/abs/physics/0604183v1

Phys Rev E 74, 026116 (2006): updated version

Physics

Biological Physics

Expanded version of physics/0508228 with additional new results

Scientific paper

10.1103/PhysRevE.74.026116

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.

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