Interplay between function and structure in complex networks

Timothy C. Jarrett, Douglas J. Ashton, Mark Fricker, and Neil F. Johnson
Phys. Rev. E 74, 026116 – Published 21 August 2006

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 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 multiring core can cease to play any role in terms of determining the average shortest path across the network.

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  • Received 31 August 2005

DOI:https://doi.org/10.1103/PhysRevE.74.026116

©2006 American Physical Society

Authors & Affiliations

Timothy C. Jarrett1, Douglas J. Ashton2, Mark Fricker3, and Neil F. Johnson1

  • 1Physics Department, Oxford University, Oxford, OX1 3PU, United Kingdom
  • 2Physics Department, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
  • 3Department of Plant Sciences, Oxford University, Oxford, OX1 3RB, United Kingdom

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Issue

Vol. 74, Iss. 2 — August 2006

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