Date of Award

Spring 1-1-2013

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Applied Mathematics

First Advisor

Juan G. Restrepo

Second Advisor

Francois G. Meyer

Third Advisor

James D. Meiss

Fourth Advisor

Aaron Clauset

Fifth Advisor

Manuel Lladser

Abstract

From biological processes to critical infrastructures and social phenomena, many complex systems may be studied as large networks of interacting components. Research investigating the important role of network topology is therefore of broad interest, where techniques may be developed, for example, to control complex dynamical processes with strategic network modications. Applications range from mitigating damage incurred to critical infrastructure (e.g., the energy, banking, and transit systems) to controlling spreading processes, including both those that are harmful (e.g., epidemics) and benecial (e.g., information dissemination). Among the many successful techniques for studying complex networks, spectral graph theory has been shown to be remarkably useful for analyzing and controlling the dynamical and robustness properties of a given network. In this thesis, I discuss my contributions to this eld, which explore the following applications: (i) The analysis of a given network's robustness to the strategic removal of nodes and/or links; (ii) The development of techniques to judiciously modify a network to tune its robustness and dynamical properties; and (iii) The introduction and analysis of a network formation process yielding networks that self-organize with enhanced spreading and robustness characteristics.

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