Relational Variables for Graph Theory

Abstract We systematically consider simple relational variables — relative variables, ratio variables and dilatational variables — for Graph Theory. We apply these to simplifying graph inequalities and elucidating a large number Graph-Theoretically significant probability-valued variables. This material has further use in developing network stucture quantifiers. It represents interaction between Similarity Geometry, and basic Shape Theory in the sense of Kendall, with Graph Theory.