Limit theorems for the weights and the degrees in anN-interactions random graph model-Reference-Cited by-同舟云学术

Limit theorems for the weights and the degrees in anN-interactions random graph model

Published:2016-01-01 Issue:1 Volume:14 Page:414-424
ISSN:2391-5455
Container-title:Open Mathematics
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Author:

Fazekas István,Porvázsnyik Bettina

Abstract

Abstract A random graph evolution based on interactions of N vertices is studied. During the evolution both the preferential attachment rule and the uniform choice of vertices are allowed. The weight of an M-clique means the number of its interactions. The asymptotic behaviour of the weight of a fixed M-clique is studied. Asymptotic theorems for the weight and the degree of a fixed vertex are also presented. Moreover, the limits of the maximal weight and the maximal degree are described. The proofs are based on martingale methods.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2016-0039/pdf

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