Skinning is a recent concept emerging from long lasting efforts to separate look-and-feel from core functional aspects in software or web design. In this paper, we propose skinnable graph drawing as a process that takes a general graph G(V,E) and computes a drawing of G from a skin of G and a signature of G. Skinnable graph drawing objective is two-fold: (1) reduce the time and effort spent re-drawing and customizing a drawing for general graphs and (2) maintain invariants in the drawing for the preservation of both personal mental maps and group mental maps. In this paper, we start by clarifying the concept of skin in the context of graph drawing, we further propose a signature of a graph as a canonical labeling of a general graph made to make skinable graph drawing possible for general graphs. We finally explain how the signature and the skin are sufficient to build a drawing of a graph.