Breast cancer has emerged as a severe public health issue and one of the main reasons for cancer-related mortality in women worldwide. Although the definitive reason for breast cancer is unknown, many genes and mutations in these genes associated with breast cancer have been identified using developed methods. The recurrence of a mutation in patients is a highly used feature for finding driver mutations. However, for various reasons, some mutations are more likely to arise than others. Sequencing analysis has demonstrated that cancer-driver genes perform across complicated pathways and networks, with mutations often arising in a modular pattern. In this work, we proposed a novel machine-learning method to study the functionality of genes in the networks derived from mutation associations, gene-gene interactions, and graph clustering for breast cancer analysis. These networks have revealed essential biological elements in the vital pathways, notably those that undergo low-frequency mutations. The statistical power of the clinical study is considerably increased when evaluating the network rather than just the effects of a single gene. The proposed method discovered key driver genes with various mutation frequencies. We investigated the function of the potential driver genes and related pathways. By presenting lower-frequency genes, we recognized breast cancer-related pathways that are less studied. In addition, we suggested a novel Monte Carlo-based algorithm to identify driver modules in breast cancer. We demonstrated our proposed modules' importance and role in critical signaling pathways in breast cancer, and this evaluation for breast cancer-related driver modules gave us an inclusive insight into breast cancer development.