Characterizing the Spectral Radius of a Sequence of Adjacency Matrices

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.

Grantor dc:publisher

Wake Forest University

Year dc:date.issued

2018

Author dc:creator

• Fries, William

• Epidemics

Language dc:language.iso

en

Handle dc:identifier.uri

http://hdl.handle.net/10339/90700

OAI identifier oai:identifier

oai:wakespace.lib.wfu.edu:10339/90700