A preferential attachment model with random initial degrees

M. Deijfen, H. Esker, van den, R.W. Hofstad, van der, G. Hooghiemstra

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

31 Citaten (Scopus)


In this paper, a random graph process {G(t)} t=1 is studied and its degree sequence is analyzed. Let {W t } t=1 be an i.i.d. sequence. The graph process is defined so that, at each integer time t, a new vertex with W t edges attached to it, is added to the graph. The new edges added at time t are then preferentially connected to older vertices, i.e., conditionally on G(t-1), the probability that a given edge of vertex t is connected to vertex i is proportional to d i (t-1)+d, where d i (t-1) is the degree of vertex i at time t-1, independently of the other edges. The main result is that the asymptotical degree sequence for this process is a power law with exponent t=min{tW,tP}, where tW is the power-law exponent of the initial degrees {W t } t=1 and tP the exponent predicted by pure preferential attachment. This result extends previous work by Cooper and Frieze.
Originele taal-2Engels
Pagina's (van-tot)41-72
TijdschriftArkiv för Matematik
Nummer van het tijdschrift1
StatusGepubliceerd - 2009

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