A preferential attachment process approaching the Rado graph

@article{Elwes2020APA,
  title={A preferential attachment process approaching the Rado graph},
  author={Richard Elwes},
  journal={Proceedings of the Edinburgh Mathematical Society},
  year={2020},
  volume={63},
  pages={443 - 455}
}
  • Richard Elwes
  • Published 29 March 2016
  • Mathematics
  • Proceedings of the Edinburgh Mathematical Society
Abstract We consider a simple preferential attachment graph process, which begins with a finite graph and in which a new (t + 1)st vertex is added at each subsequent time step t that is connected to each previous vertex u ≤ t with probability du(t)/t, where du(t) is the degree of u at time t. We analyse the graph obtained as the infinite limit of this process, and we show that, as long as the initial finite graph is neither edgeless nor complete, with probability 1 the outcome will be a copy of… Expand
Preferential Attachment Processes Approaching The Rado Multigraph
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Preferential Attachment Processes Approaching The Rado Multigraph
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If the preferential attachment process in which a multigraph is built one node at a time is asymptotically bounded above and below by linear functions in stage t, then with probability $1$ the infinite limit of the process will be isomorphic to the Rado multigraph. Expand
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