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.
@article{bwmeta1.element.doi-10_1515_math-2016-0039,
author = {Istv\'an Fazekas and Bettina Porv\'azsnyik},
title = {Limit theorems for the weights and the degrees in anN-interactions random graph model},
journal = {Open Mathematics},
volume = {14},
year = {2016},
pages = {414-424},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2016-0039}
}
István Fazekas; Bettina Porvázsnyik. Limit theorems for the weights and the degrees in anN-interactions random graph model. Open Mathematics, Tome 14 (2016) pp. 414-424. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2016-0039/