Multi-Hub Theory for Spectral Based System Design

摘要

There are a variety of systems whose properties are governed by the leading eigenvectors of the underlying system matrix. If the set of the dominant eigenvalues are clearly separated from the next largest eigenvalues, then via the corresponding leading eigenvectors, we can readily characterize the system properties. In this presentation, we will describe approach which can assure clear separation in leading eigenvalues by imposing a proper structure of the underlying matrix. Specifically, we provide bounds on eigenvalues for the hierarchical system connection structure. Based on these results, we can design hierarchical systems with assured clustering behavior or absence of it.