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

Open Mathematics (2016)

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

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## Abstract

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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.

## How to cite

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István 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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