Neural image-to-text radiology report generation systems offer the potential to improve radiology reporting by reducing the repetitive process of report drafting and identifying possible medical errors. These systems have achieved promising performance as measured by widely used NLG metrics such as BLEU and CIDEr. However, the current systems face important limitations. First, they present an increased complexity in architecture that offers only marginal improvements on NLG metrics. Secondly, these systems that achieve high performance on these metrics are not always factually complete or consistent due to both inadequate training and evaluation. Recent studies have shown the systems can be substantially improved by using new methods encouraging 1) the generation of domain entities consistent with the reference and 2) describing these entities in inferentially consistent ways. So far, these methods rely on weakly-supervised approaches (rule-based) and named entity recognition systems that are not specific to the chest X-ray domain. To overcome this limitation, we propose a new method, the RadGraph reward, to further improve the factual completeness and correctness of generated radiology reports. More precisely, we leverage the RadGraph dataset containing annotated chest X-ray reports with entities and relations between entities. On two open radiology report datasets, our system substantially improves the scores up to 14.2% and 25.3% on metrics evaluating the factual correctness and completeness of reports.