This work presents an enhanced approach to generating scene graphs by incorporating a relationship hierarchy and commonsense knowledge. Specifically, we propose a Bayesian classification head that exploits an informative hierarchical structure. It jointly predicts the super-category or type of relationship between the two objects, along with the detailed relationship under each super-category. We design a commonsense validation pipeline that uses a large language model to critique the results from the scene graph prediction system and then use that feedback to enhance the model performance. The system requires no external large language model assistance at test time, making it more convenient for practical applications. Experiments on the Visual Genome and the OpenImage V6 datasets demonstrate that harnessing hierarchical relationships enhances the model performance by a large margin. The proposed Bayesian head can also be incorporated as a portable module in existing scene graph generation algorithms to improve their results. In addition, the commonsense validation enables the model to generate an extensive set of reasonable predictions beyond dataset annotations.