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Title: Distances in preferential attachment networks
Author: Mönch, Christian
Awarding Body: University of Bath
Current Institution: University of Bath
Date of Award: 2013
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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.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available