 For each such pair, and each edge "uv" adjacent to "v" in "G", make an edge from ("v","w") to ("u","w" ± "ε") where "ε" is zero if "uv" belongs to the spanning tree and is otherwise the basis vector associated with "uv", and where the plus or minus sign is chosen according to the direction the edge is traversed.The resulting graph is independent of the choice of the spanning tree, and the same construction can also be interpreted more abstractly using the theory of homology.Using the same construction, the hexagonal tiling of the plane is the maximal abelian covering graph of the three-edge dipole graph, and the diamond cubic is the maximal abelian covering graph of the four-edge dipole.