preprint · arXiv (Cornell University) · 2019

Sublinear preferential attachment combined with the growing number of\n choices

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Abstract

We prove almost sure convergence of the maximum degree in an evolving graph\nmodel combining a growing number of local choices with sublinear preferential\nattachment. At each step in the growth of the graph, a new vertex is\nintroduced. Then we draw a random number of edges from it to existing vertices,\nchosen independently by the following rule. For each edge, we consider a sample\nof the growing size of vertices chosen with probabilities proportional to the\nsublinear function of their degrees. Then new vertex attaches to the vertex\nwith the highest degree from the sample. Depending on the growth rate of the\nsample and the sublinear function, the maximum degree could be of the sublinear\norder, of the linear order or having almost all edges drawing to it. The prove\nusing various stochastic approximation processes and a large deviation\napproach.\n

Cite this paper

APA 7

Malyshkin, Y. (2019). Sublinear preferential attachment combined with the growing number of\n choices. arXiv (Cornell University). https://doi.org/10.48550/arxiv.1911.07594

MLA 9

Malyshkin, Yury. “Sublinear preferential attachment combined with the growing number of\n choices.” arXiv (Cornell University), 2019, https://doi.org/10.48550/arxiv.1911.07594.

Chicago

Malyshkin, Yury. 2019. “Sublinear preferential attachment combined with the growing number of\n choices.” arXiv (Cornell University). https://doi.org/10.48550/arxiv.1911.07594.

Harvard

Malyshkin, Y. (2019) ‘Sublinear preferential attachment combined with the growing number of\n choices’, arXiv (Cornell University). Available at: https://doi.org/10.48550/arxiv.1911.07594.

BibTeX

@misc{malyshkin2019sublinear,
  title = {{Sublinear preferential attachment combined with the growing number of\n choices}},
  author = {Malyshkin, Yury},
  journal = {arXiv (Cornell University)},
  year = {2019},
  doi = {10.48550/arxiv.1911.07594}
}

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