The Use of Directed Graphs in Evolving Overall Measures of the Structure of a System

Structural relationships between various components of a system may be represented by digraphs. Quantitative measures are suggested which are useful in characterizing specific structures. These measures are based on the 'reachability' matrix, the 'adjacency' matrix and the 'distance' matrix of the composite structural digraphs. The choice of a measure must be based on one or more of these matrices, depending on the nature of the relationship between the elements of the system. These measures provide a suitable overall quantitative estimate of the structure for correlation studies of any structure and its performance or efficiency. This paper briefly sets out the principles involved and adumbrates possibilities of application. An example is provided to indicate the simple numerical methods involved in calculating these measures. The suggestions in this paper are indicative of the various similar measures that may be explored to suit the requirements of any specific structure.