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

• Autorzy: István Fazekas , Bettina Porvázsnyik
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 05C80: Random graphs
• 60G42: Martingales with discrete parameter

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2016
• Tom: 14
• Numer: 1
• Strony: 414-424

Daty

wydano

2016-01-01

otrzymano

2015-04-20

zaakceptowano

2016-04-20

online

2016-06-18

Twórcy

autor

István Fazekas

• Department of Applied Mathematics and Probability Theory, Faculty of Informatics, University of Debrecen, P.O. Box 400, 4002 Debrecen,

autor

Bettina Porvázsnyik

• Bettina Porvázsnyik: Department of Applied Mathematics and Probability Theory, Faculty of Informatics, University of Debrecen, P.O. Box 400, 4002 Debrecen,

Identyfikatory

DOI

10.1515/math-2016-0039