Interplay between function and structure in complex networks

Abstract

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.

Expanded version of physics/0508228 with additional new results

References in corpus (2)

• Optimal design of spatial distribution networks
• Optimal Paths in Disordered Complex Networks

Cited by in corpus (7)

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• Bio-Development of Motorway Networks in the Netherlands: A Slime Mould Approach
• The Emergence and Dynamical Evolution of Complex Transport Networks from Simple Low-Level Behaviours
• The World's Colonisation and Trade Routes Formation as Imitated by Slime Mould
• Braess like Paradox in a Small World Network
• Growth-induced mass flows in fungal networks
• Braess like Paradox on Ladder Network