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/