On the use of generating functions for topics in clustered networks

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.