In a previous work, we have developed a framework for the multimodal and hierarchical classification of images from soil remediation reports. We extended this work using Deep Metric Learning (DML) as an additional training step to improve embeddings quality and obtained 84.24% of weighted F1 score for the level 5th hierarchical level. However, the standard classifier performance metrics are insufficient to explain the decision process reasoning. So far of our knowledge, there are no methods to analyze hierarchical classification algorithms. In this work, we propose a method of graph analysis to describe the embeddings that represent the extended classifier, which we believe properly interprets the obtained results than classification metrics. We illustrate the method of analyzing hierarchical classification algorithms on private dataset, but the method remains generic enough to be used in other contexts.