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1 results

  • 5 - Connected Components in Preferential Attachment Models

  • from Part II - Connected Components in Random Graphs
  • Remco van der Hofstad, Technische Universiteit Eindhoven, The Netherlands
  • Book:
    Random Graphs and Complex Networks
    Published online:
    08 February 2024
    Print publication:
    08 February 2024, pp 189-242

  • Summary

    In this chapter we investigate the connectivity structure of preferential attachment models. We start by discussing an important tool: exchangeable random variables and their distribution described in de Finetti’s Theorem. We apply these results to Pólya urn schemes, which, in turn, we use to describe the distribution of the degrees in preferential attachment models. It turns out that Pólya urn schemes can also be used to describe the local limit of preferential attachment models. A crucial ingredient is the fact that the edges in the Pólya urn representation are conditionally independent, given the appropriate randomness. The resulting local limit is the Pólya point tree, a specific multi-type branching process with continuous types.