# MathSciDoc: An Archive for Mathematician ∫

#### TBDmathscidoc: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.
```@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.