On Arranging Elements of a Hierarchy in Graphic Form

Hierarchies are fundamental in the study of many kinds of complex systems. Methods are presented that assist in the development of a hierarchy or a set of hierarchies. Once the element set and the relations among the elements are established, the rationalizing procedure presented allows computer determination of how many separate hierarchies are represented by the relations among the elements. An example of the rationalization process is given. Two methods-the element method and the level method-are given for developing a hierarchy for a connected subordination matrix. Each method is illustrated with an example.