Motivation: Molecular interaction networks summarize complex biological processes as graphs, whose structure is informative of biological function at multiple scales. Simultaneously, omics technologies measure the variation or activity of genes, proteins, or metabolites across individuals or experimental conditions. Integrating the complementary viewpoints of biological networks and omics data is an important task in bioinformatics, but existing methods treat networks as discrete structures, which are intrinsically difficult to integrate with continuous node features or activity measures. Graph neural networks map graph nodes into a low-dimensional vector space representation, and can be trained to preserve both the local graph structure and the similarity between node features. Results: We studied the representation of transcriptional, protein-protein and genetic interaction networks in E. Coli and mouse using graph neural networks. We found that such representations explain a large proportion of variation in gene expression data, and that using gene expression data as node features improves the reconstruction of the graph from the embedding. We further proposed a new end-to-end graph feature auto-encoder which is trained on the feature reconstruction task, and showed that it performs better at predicting unobserved node features than auto-encoders that are trained on the graph reconstruction task before learning to predict node features. When applied to the problem of imputing missing data in single-cell RNAseq data, our graph feature auto-encoder outperformed a state-of-the-art imputation method that does not use protein interaction information, showing the benefit of integrating biological networks and omics data using graph representation learning.