This paper introduces a novel approach to learn visually grounded meaning representations of words as low-dimensional node embeddings on an underlying graph hierarchy. The lower level of the hierarchy models modality-specific word representations, conditioned to another modality, through dedicated but communicating graphs, while the higher level puts these representations together on a single graph to learn a representation jointly from both modalities. The topology of each graph models similarity relations among words, and is estimated jointly with the graph embedding. The assumption underlying this model is that words sharing similar meaning correspond to communities in an underlying graph in a low-dimensional space. We named this model Hierarchical Multi-Modal Similarity Graph Embedding (HM-SGE). Experimental results validate the ability of HM-SGE to simulate human similarity judgments and concept categorization, outperforming the state of the art.