Abstract: Based on generalized Voronoi diagram,the concepts of span and potential for Voronoi skeleton edges are proposed.An algorithm for constructing hierarchical Voronoi skeleton which preserves connectivity is presented.Further,the qualitative Voronoi skeleton mechanism is described, which can represent planar shape and arrangement in a unified form.As a result,this work generalizes the works of Tagare,Mayya and Ogniewicz.