A complex unit gain graph ( T -gain graph) Φ = G , φ ) is a where the function assigns number to each orientation of an edge and its inverse assigned opposite orientation. balanced if product gains oriented cycle (if any) 1. We propose two notions distance matrices D < max min Φ, for any ordering ‘<’ vertex set. characterize graphs which are independent ordering. show holds standard vertices on...

Graham and Winkler derived a formula for the determinant of distance matrix full-dimensional set n + 1 points { x 0 , … } in Hamming cube H = ( ? ) . In this article we derive D an arbitrary m It follows from more general that det ? if only vectors are affinely independent. Specializing to case provides new insights into original Winkler. A significant difference arises between cases < is noted...

DISTATIS is a generalization of classical multidimensional scaling (MDS see the corresponding entry formore details on thismethod) proposed by Abdi et al., (2005). Its goal is to analyze several distance matrices computed on the same set of objects. The name DISTATIS is derived from a technique called STATIS whose goal is to analyze multiple data sets (see the corresponding entry for more detai...