See the first two of the below (in reverse order) for my recent exposition of this.
APPLIED COMBINATORICS (Widely-Applicable Mathematics Series. Volume 0)
My new freely-available book is out here: Applied Combinatorics – Concepts of Shape
Shape (In)dependent Inequalities for Triangleland’s Jacobi and Democratic-Linear Ellipticity Quantitities
Abstract Sides and medians are both Jacobi coordinate magnitudes. These furthermore enter equably into the spherical coordinates on Kendall’s shape sphere and the Hopf coordinates. This motivates treating medians on the same footing as sides in the geometry of triangles and the ensuing Shape Theory. In this article, we consequently reformulate inequalities for the medians…
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…
Concepts of Shape 