A preferential attachment model with random initial degrees

Maria Deijfen Department of Mathematics, Stockholm University Henri van den Esker Electrical Engineering, Mathematics and Computer Science, Delft University of Technology Remco van der Hofstad Department of Mathematics and Computer Science, Eindhoven University of Technology Gerard Hooghiemstra Electrical Engineering, Mathematics and Computer Science, Delft University of Technology

TBD mathscidoc:1701.333139

Arkiv for Matematik, 47, (1), 41-72, 2007.3
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)+δ, 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 τ=min{τ_{W},τ_{P}}, where τ_{W}is the power-law exponent of the initial degrees {$W$_{$t$}}_{$t$≥1}and τ_{P}the exponent predicted by pure preferential attachment. This result extends previous work by Cooper and Frieze.
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@inproceedings{maria2007a,
  title={A preferential attachment model with random initial degrees},
  author={Maria Deijfen, Henri van den Esker, Remco van der Hofstad, and Gerard Hooghiemstra},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203623921395948},
  booktitle={Arkiv for Matematik},
  volume={47},
  number={1},
  pages={41-72},
  year={2007},
}
Maria Deijfen, Henri van den Esker, Remco van der Hofstad, and Gerard Hooghiemstra. A preferential attachment model with random initial degrees. 2007. Vol. 47. In Arkiv for Matematik. pp.41-72. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203623921395948.
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