In single-particle reconstruction methods [1], projections of macromolecules lying in randomly unknown orientations are collected by a transmission electron microscope. Often, several classes of conformations or binding states coexist in the sample. To obtain structures with high accuracy, it is required to separate the classes before reconstruction of the molecules. In this work, we use a graph-theoretic criterion based on common lines, which measures both the dissimilarity between the classes and the similarity within the classes. Projections are then sorted by optimizing this measure, without need for a reference volume or for any intermediate reconstructions, as done in most classification methods.The usefulness of this type of approach, via a combinatorial optimization of the measure, was first demonstrated in [2], but tested only on simulated projection data. We instead view the optimization as an eigen-decomposition problem, which makes it easy to account for different kinds of normalization of the measure. The work in [3] also uses eigen-decomposition, but the similarity is measured between 2D averages, and a reference volume is required to pre-sort the projections according to their angular orientation.In this work we measure the similarity between the projection data themselves and show the results for both simulated and experimental data.[1] J. Frank, Three Dimensional Electron Microscopy of Macromolecular Assemblies, Oxford, 2006[2] G.T. Herman and M. Kalinowski, Classification of heterogeneous electron microscopic projections into homogeneous subsets, Ultramicroscopy 108:327-338, 2008[3] M. Shatsky et al., Automated multi-model reconstruction from single-particle electron microscopy data, J. Struct. Biol. 170:98-108, 2010