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.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:607617 |
| Date | January 2013 |
| Creators | Mönch, Christian |
| Contributors | Morters, Peter |
| Publisher | University of Bath |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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