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The origin of power-law emergent scaling in large binary networks


  • Almond, D.P.
  • Budd, C.J.
  • Freitag, M.A.
  • Hunt, G.W.
  • McCullen, N.J.
  • Smith, N.D.


We study the macroscopic conduction properties of large but finite binary networks with conducting bonds. By taking a combination of a spectral and an averaging based approach we derive asymptotic formulae for the conduction in terms of the component proportions p and the total number of components N. These formulae correctly identify both the percolation limits and also the emergent power-law behaviour between the percolation limits and show the interplay between the size of the network and the deviation of the proportion from the critical value of p=1/2. The results compare excellently with a large number of numerical simulations.

Suggested Citation

  • Almond, D.P. & Budd, C.J. & Freitag, M.A. & Hunt, G.W. & McCullen, N.J. & Smith, N.D., 2013. "The origin of power-law emergent scaling in large binary networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 1004-1027.
  • Handle: RePEc:eee:phsmap:v:392:y:2013:i:4:p:1004-1027
    DOI: 10.1016/j.physa.2012.10.035

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