Understanding phenotype-to-genotype relationships is a grand challenge of 21st century biology with translational implications. The recently proposed "omnigenic" model postulates that effects of genetic variation on traits are mediated by core-genes and -proteins whose activities mechanistically influence the phenotype, whereas peripheral genes encode a regulatory network that indirectly affects phenotypes via core gene products. Here, we develop a positive-unlabeled graph representation-learning ensemble-approach based on a nested cross-validation to predict core-like genes for diverse diseases using Mendelian disorder genes for training. Employing mouse knockout phenotypes for external validations, we demonstrate that core-like genes display several key properties of core genes: Mouse knockouts of genes corresponding to our most confident predictions give rise to relevant mouse phenotypes at rates on par with the Mendelian disorder genes, and all candidates exhibit core gene properties like transcriptional deregulation in disease and loss-of-function intolerance. Moreover, as predicted for core genes, our candidates are enriched for drug targets and druggable proteins. In contrast to Mendelian disorder genes the new core-like genes are enriched for druggable yet untargeted gene products, which are therefore attractive targets for drug development. Interpretation of the underlying deep learning model suggests plausible explanations for our core gene predictions in form of molecular mechanisms and physical interactions. Our results demonstrate the potential of graph representation learning for the interpretation of biological complexity and pave the way for studying core gene properties and future drug development.