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Accuracy of mean-field theory for dynamics on real-world networks

James P. Gleeson1, Sergey Melnik1,2,3, Jonathan A. Ward1,4, Mason A. Porter2,3, and Peter J. Mucha5,6

  • 1MACSI, Department of Mathematics & Statistics, University of Limerick, Ireland
  • 2Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, OX1 3LB, United Kingdom
  • 3CABDyN Complexity Centre, University of Oxford, Oxford, OX1 1HP, United Kingdom
  • 4Centre for Mathematics of Human Behaviour, Department of Mathematics & Statistics, University of Reading, Reading, RG6 6AX, United Kingdom
  • 5Carolina Center for Interdisciplinary Applied Mathematics, Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599-3250, USA
  • 6Institute for Advanced Materials, Nanoscience & Technology, University of North Carolina, Chapel Hill, North Carolina 27599-3216, USA

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Phys. Rev. E 85, 026106 – Published 7 February, 2012

DOI: https://doi.org/10.1103/PhysRevE.85.026106

Abstract

Mean-field analysis is an important tool for understanding dynamics on complex networks. However, surprisingly little attention has been paid to the question of whether mean-field predictions are accurate, and this is particularly true for real-world networks with clustering and modular structure. In this paper, we compare mean-field predictions to numerical simulation results for dynamical processes running on 21 real-world networks and demonstrate that the accuracy of such theory depends not only on the mean degree of the networks but also on the mean first-neighbor degree. We show that mean-field theory can give (unexpectedly) accurate results for certain dynamics on disassortative real-world networks even when the mean degree is as low as 4.

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Phys. Rev. E 85, 026106– Published 7 February, 2012
  • Received 16 November 2010
Article part of CHORUS

©2012 American Physical Society

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