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Analytic solutions for links and triangles distributions in finite Barabási–Albert networks

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  • Ferreira, Ricardo M.
  • de Almeida, Rita M.C.
  • Brunnet, Leonardo G.

Abstract

Barabási–Albert model describes many different natural networks, often yielding sensible explanations to the subjacent dynamics. However, finite size effects may prevent from discerning among different underlying physical mechanisms and from determining whether a particular finite system is driven by Barabási–Albert dynamics. Here we propose master equations for the evolution of the degrees, links and triangles distributions, solve them both analytically and by numerical iteration, and compare with numerical simulations. The analytic solutions for all these distributions predict the network evolution for systems as small as 100 nodes. The analytic method we developed is applicable for other classes of networks, representing a powerful tool to investigate the evolution of natural networks.

Suggested Citation

  • Ferreira, Ricardo M. & de Almeida, Rita M.C. & Brunnet, Leonardo G., 2017. "Analytic solutions for links and triangles distributions in finite Barabási–Albert networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 105-110.
    • Handle: RePEc:eee:phsmap:v:466:y:2017:i:c:p:105-110
    DOI: 10.1016/j.physa.2016.08.018
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    References listed on IDEAS

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    1. Ash, J. & Newth, D., 2007. "Optimizing complex networks for resilience against cascading failure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 673-683.
    2. Barabási, Albert-László & Albert, Réka & Jeong, Hawoong, 1999. "Mean-field theory for scale-free random networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 272(1), pages 173-187.
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    Cited by:

    1. Sudbrack, Vítor & Brunnet, Leonardo G. & de Almeida, Rita M.C. & Ferreira, Ricardo M. & Gamermann, Daniel, 2018. "Master equation for the degree distribution of a Duplication and Divergence network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 588-598.

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