It is an important subject to research the functional mechanism of cancer-related genes make in formation and development of cancers. The modern methodology of data analysis plays a very important role for deducing the relationship between cancers and cancer-related genes and analyzing functional mechanism of genome. In this research, we construct mutual information networks using gene expression profiles of glioblast and renal in normal condition and cancer conditions. We investigate the relationship between structure and robustness in gene networks of the two tissues using a cascading failure model based on betweenness centrality. Define some important parameters such as the percentage of failure nodes of the network, the average size-ratio of cascading failure, and the cumulative probability of size-ratio of cascading failure to measure the robustness of the networks. By comparing control group and experiment groups, we find that the networks of experiment groups are more robust than that of control group. The gene that can cause large scale failure is called structural key gene. Some of them have been confirmed to be closely related to the formation and development of glioma and renal cancer respectively. Most of them are predicted to play important roles during the formation of glioma and renal cancer, maybe the oncogenes, suppressor genes, and other cancer candidate genes in the glioma and renal cancer cells. However, these studies provide little information about the detailed roles of identified cancer genes.