Understanding how oncogenic mutations rewire regulatory-protein networks is important for rationalizing the mechanisms of oncogenesis and for individualizing anticancer treatments. We report a chemical phosphoproteomics method to elucidate the topology of kinase-signaling networks in mammalian cells. We identified >6,000 protein phosphorylation sites that can be used to infer >1,500 kinase-kinase interactions and devised algorithms that can reconstruct kinase network topologies from these phosphoproteomics data. Application of our methods to primary acute myeloid leukemia and breast cancer tumors quantified the relationship between kinase expression and activity, and enabled the identification of hitherto unknown kinase network topologies associated with drug-resistant phenotypes or specific genetic mutations. Using orthogonal methods we validated that PIK3CA wild-type cells adopt MAPK-dependent circuitries in breast cancer cells and that the kinase TTK is important in acute myeloid leukemia. Our phosphoproteomic signatures of network circuitry can identify kinase topologies associated with both phenotypes and genotypes of cancer cells.