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April 2009 A preferential attachment model with random initial degrees
Maria Deijfen, Henri van den Esker, Remco van der Hofstad, Gerard Hooghiemstra
Ark. Mat. 47(1): 41-72 (April 2009). DOI: 10.1007/s11512-007-0067-4

## Abstract

In this paper, a random graph process {G(t)}t≥1 is studied and its degree sequence is analyzed. Let {Wt}t≥1 be an i.i.d. sequence. The graph process is defined so that, at each integer time t, a new vertex with Wt 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 di(t-1)+δ, where di(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 τ=min{τWP}, where τW is the power-law exponent of the initial degrees {Wt}t≥1 and τP the exponent predicted by pure preferential attachment. This result extends previous work by Cooper and Frieze.

## Version Information

In the published form of the paper, the proof of Proposition 2.1 is incomplete. For the complete proof, see the arXiv version (arXiv:0705.4151) of this paper.

## Citation

Maria Deijfen. Henri van den Esker. Remco van der Hofstad. Gerard Hooghiemstra. "A preferential attachment model with random initial degrees." Ark. Mat. 47 (1) 41 - 72, April 2009. https://doi.org/10.1007/s11512-007-0067-4

## Information

Received: 1 March 2007; Published: April 2009
First available in Project Euclid: 31 January 2017

zbMATH: 1182.05107
MathSciNet: MR2480915
Digital Object Identifier: 10.1007/s11512-007-0067-4