The Bass Diffusion Model on Finite Barabasi-Albert Networks
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 ex...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/6352657 |
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| author | M. L. Bertotti G. Modanese |
| author_facet | M. L. Bertotti G. Modanese |
| author_sort | M. L. Bertotti |
| collection | DOAJ |
| description | 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 104 nodes. |
| format | Article |
| id | doaj-art-c0adf7fdb59941e594e690c328eeb49c |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-c0adf7fdb59941e594e690c328eeb49c2025-02-03T01:32:57ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/63526576352657The Bass Diffusion Model on Finite Barabasi-Albert NetworksM. L. Bertotti0G. Modanese1Free University of Bolzano-Bozen, Faculty of Science and Technology, 39100 Bolzano, ItalyFree University of Bolzano-Bozen, Faculty of Science and Technology, 39100 Bolzano, ItalyUsing 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 104 nodes.http://dx.doi.org/10.1155/2019/6352657 |
| spellingShingle | M. L. Bertotti G. Modanese The Bass Diffusion Model on Finite Barabasi-Albert Networks Complexity |
| title | The Bass Diffusion Model on Finite Barabasi-Albert Networks |
| title_full | The Bass Diffusion Model on Finite Barabasi-Albert Networks |
| title_fullStr | The Bass Diffusion Model on Finite Barabasi-Albert Networks |
| title_full_unstemmed | The Bass Diffusion Model on Finite Barabasi-Albert Networks |
| title_short | The Bass Diffusion Model on Finite Barabasi-Albert Networks |
| title_sort | bass diffusion model on finite barabasi albert networks |
| url | http://dx.doi.org/10.1155/2019/6352657 |
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