Distances in Preferential Attachment Networks

  • Christian Mönch

Student thesis: Doctoral ThesisPhD


Preferential attachment networks with power law degree sequence undergo a phase transition when the power law exponent τ changes. For τ > 3 typical distances in the network are logarithmic in the size of the network and for 2 < τ < 3 they are doubly logarithmic. In this thesis, we identify the correct scaling constant for τ ∈ (2, 3) and discover a surprising dichotomy between preferential attachment networks and networks without preferential attachment. This contradicts previous conjectures of universality. Moreover, using a model recently introduced by Dereich and Mörters, we study the critical behaviour at τ = 3, and establish novel results for the scale of the typical distances under lower order perturbations of the attachment function.
Date of Award4 Dec 2013
Original languageEnglish
Awarding Institution
  • University of Bath
SupervisorPeter Morters (Supervisor)


  • scale free networks
  • preferential attachment

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