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Many object‐oriented metrics have been proposed in the literature to measure various structural properties of object‐oriented software. Furthermore, many centrality measures have been introduced to identify central nodes in large networks. However, few studies have used them to measure dependencies in software systems. In fact, centrality measures, as opposed to most traditional object‐oriented metrics that mainly focus on intrinsic properties of classes, can be used to better model the control flow and to identify the most important classes in a software system. This paper aims (1) to investigate the relationships between object‐oriented metrics and centrality measures and (2) to explore the ability of their combination to support fault‐proneness prediction from different perspectives (fault‐prone classes, fault severity, and number of faults). Many studies in the literature have addressed the prediction of fault‐prone classes, from different perspectives, using object‐oriented metrics. The main motivation here is in fact to investigate if the information captured by centrality measures is related to fault proneness and complementary to the information captured by object‐oriented metrics and to investigate if the combination of object‐oriented metrics and centrality measures improves the performance of fault‐proneness prediction significantly. We used size, complexity, and coupling object‐oriented metrics in addition to various centrality measures. We collected data from 20 different versions of five open‐source Java software systems. We first studied the relationships between selected metrics and their relationships to fault proneness. Then, we built different models to predict fault‐prone classes using several machine learning algorithms. In addition, we built models to predict if a class contains a high severity fault, and the number of faults in a class. Results indicate that using centrality measures in combination with object‐oriented metrics improves the prediction of fault‐prone classes as well as the prediction of the number of faults in a class. However, the combination has no significant impact, according to the data we collected, on the quality of the prediction of fault severity. Moreover, using centrality measures in combination with object‐oriented metrics also improves the prediction performance of fault proneness and the number of faults in both cross‐version and cross‐system validation.