Skinning is a recent concept emerging from long lasting efforts to separate look-and-feel from core functional aspects in software engineering 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 from a skin compatible with a signature of G. Skinnable graph drawing is designed to address the drawing of general graphs having no particular node labeling. Skinnable graph drawing motivations include (1) enable reuse and share of customized drawings, (2) preserve mental maps by maintaining some visual graph structures invariant and (3) facilitate the use of different conventional drawings for the same graphs to reconcile different visual perspectives on similar graph structures. In this paper, we revise useful definitions for skinnable graph drawing and report the results of a case study based on sixteen well-known graphs as an illustration of signature computations and a proof of concept of the skinnable graph drawing approach.