Ion chromatography experiments on carbon clusters have provided a powerful tool for characterizing the products of the laser ablation of graphite. Using this technique, several families of carbon clusters have been observed, and their role in a plausible fullerene formation process has been hypothesized. In this work, we have examined the experimental mobility results from a theoretical perspective. Our most interesting finding is the existence of a family of three-dimensional 2+4 cycloaddition products whose members match the experimental mobilities of the so-called "ring III" family over a range of cluster sizes, whereas previous studies have asserted that the "ring III" clusters are planar. In agreement with previous research, we find that the "ring I" and "ring II" families consist of monocyclic and bicyclic rings, respectively. However, these families should be broadly defined so as to include ring structures with carbon branches, because short carbon branches have only a negligible effect on cluster mobility.