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

Open Mathematics

Porvázsnyik Bettina¹  Fazekas István² 

[1] Bettina Porvázsnyik: Department of Applied Mathematics and Probability Theory, Faculty of Informatics, University of Debrecen, P.O. Box 400, 4002 Debrecen, Hungary;Department of Applied Mathematics and Probability Theory, Faculty of Informatics, University of Debrecen, P.O. Box 400, 4002 Debrecen, Hungary;

关键词: random graph;    preferential attachment;    scale-free;    power law;    submartingale;    05c80;    60g42;   

DOI  :  10.1515/math-2016-0039

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown