Genome wide association studies (GWAS) of human diseases have generally identified many loci associated with risk with relatively small effect sizes. The omnigenic model attempts to explain this observation by suggesting that diseases can be thought of as networks, where genes with direct involvement in disease-relevant biological pathways are named 'core genes', while peripheral genes influence disease risk via their interactions or regulatory effects on core genes. Here, we demonstrate a method for identifying candidate core genes solely from genes in or near disease-associated SNPs (GWAS hits) in conjunction with protein-protein interaction network data. Applied to 1,381 GWAS studies from 5 ancestries, we identify a total of 1,865 candidate core genes in 343 GWAS studies. Our analysis identifies several well-known disease-related genes that are not identified by GWAS, including BRCA1 in Breast Cancer, Amyloid Precursor Protein (APP) in Alzheimer's Disease, INS in A1C measurement and Type 2 Diabetes, and PCSK9 in LDL cholesterol, amongst others. Notably candidate core genes are preferentially enriched for disease relevance over GWAS hits and are enriched for both Clinvar pathogenic variants and known drug targets-consistent with the predictions of the omnigenic model. We subsequently use parent term annotations provided by the GWAS catalog, to merge related GWAS studies and identify candidate core genes in over-arching disease processes such as cancer-where we identify 109 candidate core genes.