Before revision:  We found that graph embeddings trained on transcription and PPI networks can explain more than 50 and 40 percent, respectively, of the variance in gene expression data, thus confirming the relationship between network structure and gene expression value. Additionally, for the task of predicting gene expression values using GNNs, with and without additional expression training data, we found that the message passing scheme of GNNs is able to obtain the lowest mean squared error between the tested models both in prediction of unseen test values, and in an auto-encoder scheme for reconstruction of the feature matrix of expression values .
After revision:  We found that graph embeddings trained on transcription and PPI networks can explain more than 50 and 40 percent, respectively, of the variance 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 scheme for reconstruction of the feature matrix of expression values .