Arkiv för Matematik

A preferential attachment model with random initial degrees

Maria Deijfen, Henri van den Esker, Remco van der Hofstad, and Gerard Hooghiemstra

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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.

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Ark. Mat., Volume 47, Number 1 (2009), 41-72.

Received: 1 March 2007
First available in Project Euclid: 31 January 2017

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2008 © Institut Mittag-Leffler


Deijfen, Maria; van den Esker, Henri; van der Hofstad, Remco; Hooghiemstra, Gerard. A preferential attachment model with random initial degrees. Ark. Mat. 47 (2009), no. 1, 41--72. doi:10.1007/s11512-007-0067-4.

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