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Title: Colouring, centrality and core-periphery structure in graphs
Author: Rombach, Michaela Puck
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2013
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Krivelevich and Patkós conjectured in 2009 that χ(G(n, p)) ∼ χ=(G(n, p)) ∼ χ∗=(G(n, p)) for C/n < p < 1 − ε, where ε > 0. We prove this conjecture for n−1+ε1 < p < 1 − ε2 where ε1, ε2 > 0. We investigate several measures that have been proposed to indicate centrality of nodes in networks, and find examples of networks where they fail to distinguish any of the vertices nodes from one another. We develop a new method to investigate core-periphery structure, which entails identifying densely-connected core nodes and sparsely-connected periphery nodes. Finally, we present an experiment and an analysis of empirical networks, functional human brain networks. We found that reconfiguration patterns of dynamic communities can be used to classify nodes into a stiff core, a flexible periphery, and a bulk. The separation between this stiff core and flexible periphery changes as a person learns a simple motor skill and, importantly, it is a good predictor of how successful the person is at learning the skill. This temporally defined core-periphery organisation corresponds well with the core- periphery detected by the method that we proposed earlier the static networks created by averaging over the subjects dynamic functional brain networks.
Supervisor: Porter, Mason Alexander; Scott, Alex D. Sponsor: James S. McDonnell Foundation
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Combinatorics ; Statistical mechanics,structure of matter (mathematics) ; Probability theory and stochastic processes ; Mathematical biology ; Information and communication,circuits (mathematics) ; Computer science (mathematics) ; graphs ; networks ; probability ; colouring ; algorithms ; random ; core-periphery ; centrality ; brain