A generalized computational method for folding proteins with a fully transferable potential and geometrically realistic all-atom model is presented and tested on seven helix bundle proteins. The protocol, which includes graph-theoretical analysis of the ensemble of resulting folded conformations, was systematically applied and consistently produced structure predictions of approximately 3 A without any knowledge of the native state. To measure and understand the significance of the results, extensive control simulations were conducted. Graph theoretic analysis provides a means for systematically identifying the native fold and provides physical insight, conceptually linking the results to modern theoretical views of protein folding. In addition to presenting a method for prediction of structure and folding mechanism, our model suggests that an accurate all-atom amino acid representation coupled with a physically reasonable atomic interaction potential and hydrogen bonding are essential features for a realistic protein model.