In earlier papers (Wyman, 1975a, b, 1981) I have called attention to the existence of a group of linkage potentials derivable from one another by a corresponding group of Legendre transformations. These potentials are applicable to any system in a state of equilibrium but are especially useful in the study of the behaviour, or, as we may say, the functional chemistry, of a macromolecule in the presence of its ligands. In this paper I show how these potentials may be represented by a set of contour graphs which embody the results of observation and are transformable into one another by a group of graphical permutations equivalent to the Legendre group.