Heterogeneity across cancer makes it difficult to find driver genes with intermediate (2-20%) and low frequency (<2%) mutations 1 , and we are potentially missing entire classes of networks (or pathways) of biological and therapeutic value. Here, we quantify the extent to which cancer genes across 21 tumor types have an increased burden of mutations in their immediate gene network derived from functional genomics data. We formalize a classifier that accurately calculates the significance level of a gene's network mutation burden (NMB) and show it can accurately predict known cancer genes and recently proposed driver genes in the majority of tested tumours. Our approach predicts 62 putative cancer genes, including 35 with clear connection to cancer and 27 genes, which point to new cancer biology. NMB identifies proportionally more (4x) low-frequency mutated genes as putative cancer genes than gene-based tests, and provides molecular clues in patients without established driver mutations. Our quantitative and comparative analysis of pan-cancer networks across 21 tumour types gives new insights into the biological and genetic architecture of cancers and enables additional discovery from existing cancer genomes. The framework we present here should become increasingly useful with more sequencing data in the future.