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

被引：4

作者：

Fazekas, Istvan ^{[1
]}

Porvazsnyik, Bettina ^{[1
]}

机构：

[1] Univ Debrecen, Fac Informat, Dept Appl Math & Probabil Theory, POB 400, H-4002 Debrecen, Hungary

来源：

OPEN MATHEMATICS | 2016年 / 14卷

关键词：

Random graph; Preferential attachment; Scale-free; Power law; Submartingale;

D O I：

10.1515/math-2016-0039

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页码：414 / 424

页数：11

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