Integrating Past, Present, and Future Approaches - Spatial Mathematics: Theory and Practice through Mapping - page 235

Figure 10.15 Results of analysis for the optimal site for a high-speed Internet café in
the City and County of Denver. The analysis resulted in two neighborhoods being
under consideration, shown in red, near Regis University (A) and the University
of Denver (B). The final site selected was the area with the youngest median age,
near the University of Denver, shown in yellow. Source of base map: Esri software.
bus routes, and so on. To take full advantage of considering all of these factors
requires a keen knowledge of both mathematics and geography.
10.5 Graph theory and topology: Discrete and continuous
spatial mathematics
The “practice” given above involves finding routes through geographic space
and it draws on the intuition of the reader to understand what “routing” might
mean, based on real-world experience. The science of “network analysis” and
the mathematics of “graph theory” formalize and systematize ideas such as
routing. They are broad and complex disciplines (Harary, 1969; Arlinghaus,
Arlinghaus, and Harary, 2002).
A graph is a mathematical structure formed from a collection of nodes (verti-
ces) and a collection of edges joining pairs of nodes. (Please do not confuse
this sort of graph with graphs of functions.) The edges may show direction,
as in the case of “going” or “coming back” on a trip; or they may not show