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The Bass Diffusion Model on Finite Barabasi-Albert Networks

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  • M. L. Bertotti
  • G. Modanese

Abstract

Using a heterogeneous mean-field network formulation of the Bass innovation diffusion model and recent exact results on the degree correlations of Barabasi-Albert networks, we compute the times of the diffusion peak and compare them with those on scale-free networks which have the same scale-free exponent but different assortativity properties. We compare our results with those obtained for the SIS epidemic model with the spectral method applied to adjacency matrices. It turns out that diffusion times on finite Barabasi-Albert networks are at a minimum. This may be due to a little-known property of these networks: whereas the value of the assortativity coefficient is close to zero, they look disassortative if one considers only a bounded range of degrees, including the smallest ones, and slightly assortative on the range of the higher degrees. We also find that if the trickle-down character of the diffusion process is enhanced by a larger initial stimulus on the hubs (via a inhomogeneous linear term in the Bass model), the relative difference between the diffusion times for BA networks and uncorrelated networks is even larger, reaching, for instance, the 34% in a typical case on a network with nodes.

Suggested Citation

  • M. L. Bertotti & G. Modanese, 2019. "The Bass Diffusion Model on Finite Barabasi-Albert Networks," Complexity, Hindawi, vol. 2019, pages 1-12, April.
  • Handle: RePEc:hin:complx:6352657
    DOI: 10.1155/2019/6352657
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    References listed on IDEAS

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    1. Bertotti, M.L. & Brunner, J. & Modanese, G., 2016. "The Bass diffusion model on networks with correlations and inhomogeneous advertising," Chaos, Solitons & Fractals, Elsevier, vol. 90(C), pages 55-63.
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    4. P. Van Mieghem & H. Wang & X. Ge & S. Tang & F. A. Kuipers, 2010. "Influence of assortativity and degree-preserving rewiring on the spectra of networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 76(4), pages 643-652, August.
    5. Babak Fotouhi & Michael Rabbat, 2013. "Degree correlation in scale-free graphs," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 86(12), pages 1-19, December.
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    Cited by:

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