More and more the world is being described as graphs---as connections between people, places, and ideas---since they provide a richer model than simply understanding each item in isolation. In order to help analysts understand these graphs, researchers have developed and studied a large number of graph visualization techniques. This variety of techniques presents solutions to a breadth of graph analysis tasks, but it introduces a new issue: complexity. The variety introduces both the complexity of comparing techniques in an objective way and the engineering complexity of implementing so many techniques. In this thesis, I present graph-level operations models (or GLO models) as an elegant solution to these challenges. A GLO model consists of a model of visual elements and a set of functions (GLOs) that manipulate those elements. I introduce GLOv1 and GLOv2, GLO models derived from six hand-picked graph visualization techniques and twenty-nine techniques derived from a review of 430 graph visualization publications, respectively. I show how to use GLOs to define graph visualization techniques, including a model's original seed techniques as well as novel techniques. I demonstrate the analysis potential of the GLO model by clustering the twenty-nine seed techniques using two different GLO-based schemes. Finally, I demonstrate the practical engineering potential of the model through an open-source Javascript implementation (GLO.js) and two applications built atop the implementation for exploring a graph and discovering novel techniques using GLOs (GLO-STIX and GLO-CLI).Ph.D
