Malignant cell transformation and the underlying reprogramming of gene expression require the cooperation of multiple oncogenic mutations. This cooperation is reflected in the synergistic regulation of non-mutant downstream genes, so-called cooperation response genes (CRGs). CRGs affect diverse hallmark features of cancer cells and are not known to be functionally connected. However, they act as critical mediators of the cancer phenotype at an unexpectedly high frequency >50%, as indicated by genetic perturbations. Here, we demonstrate that CRGs function within a network of strong genetic interdependencies that are critical to the malignant state. Our network modeling methodology, TopNet, takes the approach of incorporating uncertainty in the underlying gene perturbation data and can identify non-linear gene interactions. In the dense space of gene connectivity, TopNet reveals a sparse topological gene network architecture, effectively pinpointing functionally relevant gene interactions. Thus, among diverse potential applications, TopNet has utility for identification of non-mutant targets for cancer intervention.