On rigidity and realizability of weighted graphs Original Research Article

Recently, a new characterization of rigid graphs was introduced using Euclidean distance matrices (EDMs) [A.Y. Alfakih, Linear Algebra Appl. 310 (2000) 149]. In this paper, we address the computational aspects of this characterization. Also we present a characterization of graphs which are realizable in image for some 1less-than-or-equals, slantrless-than-or-equals, slantn−2 but not realizable in image, where n is the number of nodes.