In this paper, we present a novel graph construction method and demonstrate its usage in a broad range of applications starting from a relatively simple single-surface segmentation and ranging to very complex multi-surface multi-object graph based image segmentation. Inspired by the properties of electric field direction lines, the proposed method for graph construction is inherently applicable to n-D problems. In general, the electric field direction lines are used for graph “column” construction. As such, our method is robust with respect to the initial surface shape and the graph structure is easy to compute. When applied to cross-surface mapping, our approach can generate one-to-one and every-to-every vertex correspondent pairs between the regions of mutual interaction, which is a substantially better solution compared with other surface mapping techniques currently used for multi-object graph-based image segmentation.