The human brain is a complex organ that consists of several regions each with a unique gene expression pattern. Our intent in this study was to construct a gene co-expression network (GCN) for the normal brain using RNA expression profiles from the Genotype-Tissue Expression (GTEx) project. The brain GCN contains gene correlation relationships that are broadly present in the brain or specific to thirteen brain regions, which we later combined into six overarching brain mini-GCNs based on the brain's structure. Using the expression profiles of brain region-specific GCN edges, we determined how well the brain region samples could be discriminated from each other, visually with t-SNE plots or quantitatively with the Gene Oracle deep learning classifier. Next, we tested these gene sets on their relevance to human tumors of brain and non-brain origin. Interestingly, we found that genes in the six brain mini-GCNs showed markedly higher mutation rates in tumors relative to matched sets of random genes. Further, we found that cortex genes subdivided Head and Neck Squamous Cell Carcinoma (HNSC) tumors and Pheochromocytoma and Paraganglioma (PCPG) tumors into distinct groups. The brain GCN and mini-GCNs are useful resources for the classification of brain regions and identification of biomarker genes for brain related phenotypes.