Abstract: Combinatorial graphs are very naturally applied to molecules, since the vertices are atoms and the edges are covalent bonds connecting them. However the graph of a molecule fails to capture its three dimensional shape, which is so important to its function. We introduce an extension of the mathematical idea of a graph which allows us to fully describe the shape of biological molecules, and in a chemically intuitive way. This provides a new interpretation of the Z-matrix, a data structure used in computational chemistry to specify molecular geometry. Our theory allows us to generalize in a canonical way the chemical internal coordinate systems of Z-matrix type, and this generalization leads to useful flexibility chemically, as well as several interesting questions in combinatorial graph theory. We will illustrate our theory with examples of "3D molecules" from biochemistry, namely amino acids, nucleotides, and glucose.