Zero-shot learning relies on semantic class representations such as attributes or pretrained embeddings to predict classes without any labeled examples. We propose to learn class representations from common sense knowledge graphs. Common sense knowledge graphs are an untapped source of explicit high-level knowledge that requires little human effort to apply to a range of tasks. To capture the knowledge in the graph, we introduce ZSL-KG, a framework based on graph neural networks with non-linear aggregators to generate class representations. Whereas most prior work on graph neural networks uses linear functions to aggregate information from neighboring nodes, we find that non-linear aggregators such as LSTMs or transformers lead to significant improvements on zero-shot tasks. On two natural language tasks across three datasets, ZSL-KG shows an average improvement of 9.2 points of accuracy versus state-of-the-art methods. In addition, on an object classification task, ZSL-KG shows a 2.2 accuracy point improvement versus the best methods that do not require hand-engineered class representations. Finally, we find that ZSL-KG outperforms the best performing graph neural networks with linear aggregators by an average of 3.8 points of accuracy across these four datasets.