We have developed a new methodology for characterizing the solvent cluster structures which occur in a pure supercritical fluid in its compressible regime. This methodology takes advantage of the time scale separation which exists between collective-cluster and individual-solvent-atom motions in order to classify atoms according to their "instantaneous" local environments. The resultant picture is of a fluid having density inhomogeneities on a mesoscopic length scale-i.e., clusters and cavities. Calculation of partial radial distribution functions shows that atoms residing in different density domains have very different equilibrium structural properties, information which is not available from the usual total radial distribution function. For example, for a 2-dimensional Lennard-Jones fluid at a reduced temperature T-r = 1.06 the nearest neighbor coordination number in a high density domain is 4.2, whereas in a low density domain it is only 1.0. We have also found that, for such clustering fluids that in a finite volume system there is an ensemble independent [within tenors of O(1/N)], nonstructural long-range correlation which arises from an excluded volume effect. This long range correlation enables us to determine the average domain size, volume fraction and density for both the high and low density domains.