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
收藏
页码：414 / 424
页数：11
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