The asymptotic behaviour of the weights and the degrees in an N-interactions random graph model

2014/05/06 by Fazekas, István, Porvázsnyik, Bettina
#05C80 #60G42 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1405.1267

Abstract

A random graph evolution based on the interactions of N vertices is studied. During the evolution both the preferential attachment method and the uniform choice of vertices are allowed. The weight of a vertex means the number of its interactions. The asymptotic behaviour of the weight and the degree of a fixed vertex, moreover the limit of the maximal weight and the maximal degree are described. The proofs are based on martingale methods.

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