Graph

Our research focuses on developing design-oriented analytical tools that enable us to bet-ter understand how a network comprising dynamic and static elements behaves when it is set in oscillatory motion, and how the interconnection topology relates to the spectral properties of the system. Such oscillatory networks are ubiquitous, extending from minia-ture electronic circuits to large-scale power networks. We tap into the rich mathematical literature on graph spectra, and develop theoretical ex-tensions applicable to networks containing nodes that have finite nonnegative weights— including nodes of zero weight, which occur naturally in the context of power networks. We develop new spectral graph-theoretic results spawned by our engineering interests, in-cluding generalizations (to node-weighted graphs) of various structure-based eigenvalue bounds. The central results of this thesis concern the phenomenon of dynamic coherency, in which clusters of vertices move in unison relative to each other. Our research exposes the relation between coherency and network structure and parameters. We study both approximat