A graph theory interpretation of nodal regions

Abstract

The techniques defined in this paper will divide a set of cities into subgroups which specify a central place and its subordinate hierarchy. The association between cities is not the only system which may be defined as a network of points and lines. Nations or states may be thought of as points with migrations or commodity flows as lines. The important step in the employment of abstract linear graph analysis is the assignment of plausible meaning to the points and lines, preferably in terms of some real world phenomena. The usefulness of the attributes and the interpretation of the resulting hierarchy depends on the correspondence between an empirical example using graph theory analysis and other knowledge of the phenomena. The procedure described in this paper may be employed in a variety of ways, but the application is valid only when significant theoretical conclusions are produced and verified empirically.