On the use of generating functions for topics in clustered networks

  • Peter Stephen Mann

Student thesis: Doctoral Thesis (PhD)

Abstract

In this thesis we relax the locally tree-like assumption of configuration model
random networks to examine the properties of clustering, and the effects
thereof, on bond percolation. We introduce an algorithmic enumeration
method to evaluate the probability that a vertex remains unattached to the giant
connected component during percolation. The properties of the non-giant,
finite components of clustered networks are also examined, along with the
degree correlations between subgraphs. In a second avenue of research, we
investigate the role of clustering on 2-strain epidemic processes under various
disease interaction schedules. We then examine an 𝑁-generation epidemic by
performing repeated percolation events.
Date of Award15 Jun 2022
Original languageEnglish
Awarding Institution
  • University of St Andrews
SupervisorSimon Andrew Dobson (Supervisor)

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