Software fault datasets such as Defects4J provide for each individual fault its location and repair, but do not characterize the faults. Current classifications use the repairs as proxies, but these do not capture the intrinsic nature of the fault. In this paper, we propose a new, direct fault classification scheme based on the control- and data-flow graph representations of programs. Our scheme comprises six control-flow and two data-flow fault classes. We manually apply this scheme to 488 faults from seven projects in the Defects4J dataset. We find that the majority of the faults are assigned between one and three classes. We also find that one of the data-flow fault classes (definition fault) is the most common individual class but that the majority of faults are classified with at least one control-flow fault class. Our proposed classification can be applied to other fault datasets and can be used to improve fault localization and automated program repair techniques for specific fault classes.