Geographically embedded networks (GENets) are systems of physical and abstract linked relationships contained wholly or partially within geographic space. The purpose of this dissertation is to examine the question, "what are the particular characteristics of networks in geography?" To uncover such properties, a series of network case studies is examined and each translated into computational data structures or workflows. Constrained as computational models, the cases are assessed and compared for patterns and common approaches. The modeling serves, 1) as a methodological template for the discovery of network properties, and 2) to reveal an initial set of characteristics for consideration based on the contemporary state of quantitative geographical analysis. The use cases are examined first by focusing on data structures and second through analytical workflows.

The data structure use cases were selected to represent diverse GENet conditions and include Minard's map of Napoleon's March on Moscow, a Census table of state-to-state human migration, and a GIS dataset of the flow routes in Kentucky's Mammoth Cave karst watershed. The analytical workflow use cases include an optimization problem (shortest path calculation), a process model (stream network generation from an elevation model), a simulation (growth along an urban corridor), and a GIS feature comparison (selection of streets bounding a city block). Commonalities from the data structure cases are distilled into a general model, but the analytical cases cannot be similarly reconciled. In order to make the geographic aspects of the analytical cases explicit, the cases are evaluated against a set of tests for spatial models devised by Goodchild (2012).

From the case studies and tests, GENet characteristics can be subdivided into two categories: those that are properties of network with respect to the physical environment and those that are properties of representation. GENets with arcs or nodes that physically exist in the environment may exhibit characteristics of constituent heterogeneity and areal interaction. GENets representations are affected by issues of scale and spatial uncertainty. To evaluate these characteristics in a GIS implementation, an itinerary planning GENet problem, the Geyser Travel Problem, is introduced. The problem offers a practical application of GENet workflows in GIS and an avenue for discussion of associated best practices.