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Spectral Theory for the Robustness and Dynamical Properties of Complex Networks

Faculty Advisor: Juan G. Restrepo

Dane Taylor

Applied Mathematics Ph.D. Program,Ìý

Date and time:Ìý

Tuesday, April 9, 2013 - 12:30pm

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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
modifications. 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 beneficial (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 field,
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.