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

István Fazekas; Bettina Porvázsnyik

Open Mathematics (2016)

- Volume: 14, Issue: 1, page 414-424
- ISSN: 2391-5455

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topIstván Fazekas, and Bettina Porvázsnyik. "Limit theorems for the weights and the degrees in anN-interactions random graph model." Open Mathematics 14.1 (2016): 414-424. <http://eudml.org/doc/281193>.

@article{IstvánFazekas2016,

abstract = {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.},

author = {István Fazekas, Bettina Porvázsnyik},

journal = {Open Mathematics},

keywords = {Random graph; Preferential attachment; Scale-free; Power law; Submartingale; random graph; preferential attachment; scale-free random graph; power law; submartingale},

language = {eng},

number = {1},

pages = {414-424},

title = {Limit theorems for the weights and the degrees in anN-interactions random graph model},

url = {http://eudml.org/doc/281193},

volume = {14},

year = {2016},

}

TY - JOUR

AU - István Fazekas

AU - Bettina Porvázsnyik

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

JO - Open Mathematics

PY - 2016

VL - 14

IS - 1

SP - 414

EP - 424

AB - 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.

LA - eng

KW - Random graph; Preferential attachment; Scale-free; Power law; Submartingale; random graph; preferential attachment; scale-free random graph; power law; submartingale

UR - http://eudml.org/doc/281193

ER -

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