| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Leipzig, Inst Math, Leipzig - Germany
[2] PUC Chile, Macul - Chile
[3] Univ Fed Minas Gerais, Dept Matemat, Belo Horizonte, MG - Brazil
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | RANDOM STRUCTURES & ALGORITHMS; v. 57, n. 3 MAY 2020. |
| Web of Science Citations: | 0 |
| Abstract | |
In this work we prove general bounds for the diameter of random graphs generated by a preferential attachment model whose parameter is a function f:N ->{[}0,1] that drives the asymptotic proportion between the numbers of vertices and edges. These results are sharp when f is a regularly varying function at infinity with strictly negative index of regular variation -gamma. For this particular class, we prove a characterization for the diameter that depends only on -gamma. More specifically, we prove that the diameter of such graphs is of order 1/gamma with high probability, although its vertex set order goes to infinity polynomially. Sharp results for the diameter for a wide class of slowly varying functions are also obtained. (AU) | |
| FAPESP's process: | 15/18930-0 - Decoupling in correlated percolation models |
| Grantee: | Caio Teodoro de Magalhães Alves |
| Support Opportunities: | Scholarships abroad - Research Internship - Post-doctor |
| FAPESP's process: | 13/24928-2 - Random walks and dependent percolation |
| Grantee: | Caio Teodoro de Magalhães Alves |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |