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Characterizing the Spectral Radius of a Sequence of Adjacency Matrices

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abstract
In this paper we explore the introductory theory of modeling epidemics on networks and the significance of the spectral radius in their analysis. We look to establish properties of the spectral radius that would better inform how an epidemic might spread over such a network. We construct a specific transformation of networks that describe a transition from a star network to a path network. For the sequence of adjacency matrices that describe this transition, we show the spectral radius of these graphs can be given in a simple algebraic equation. Using this equation we show the spectral radius increases as the star unfolds and establish bounds on the spectral radius for each network.
subject
Epidemics
Linear Algebra
Spectral Graph Theory
contributor
Fries, William (author)
Jiang, Miaohua (committee chair)
Berenhaut, Kenneth (committee member)
Ballard, Grey (committee member)
date
2018-05-24T08:36:00Z (accessioned)
2018-05-24T08:36:00Z (available)
2018 (issued)
degree
Mathematics and Statistics (discipline)
identifier
http://hdl.handle.net/10339/90700 (uri)
language
en (iso)
publisher
Wake Forest University
title
Characterizing the Spectral Radius of a Sequence of Adjacency Matrices
type
Thesis

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