Background: Triple-negative breast cancer (TNBC) is an aggressive type of breast cancer (BC), and its diagnosis is associated with negative expression of hormone receptors and HER2/neu. It consists of 10-20% of all BCs diagnosed. Methods and materials: This study focuses on three groups with different pathology: group one showed complete triple-negative HER2 expression with IHC of BC; groups two and three included patients with ER-, PR-, and HER2 1+ , and ER-, PR-, and HER2 2+ with a negative FISH test. These three groups were compared from the point of prognosis, which consisted of tumor size, patients' age, lymphatic, vascular and perineural invasion, organ metastasis, number of lymph nodes involvement, and the survival rate. Results: A total of 459 TNBC patients were enrolled, of which 268 were placed in the HER2 0 group, 146 in the HER2 1+ group, and 45 in the HER2 2+ group. Distant metastasis and recurrence rate were more common in HER2 0 patients, but bone metastasis was more common in patients with low HER2 expression. All patients with HER2 0 had a smaller tumor size at the time of BC diagnosis in comparison to patients in the low HER2 expression group. Patients with HER2 2+ had less lymphatic and vascular invasion as well as axillary lymph nodes involvement, but larger tumor size at presentation, resulting in a lower rate of recurrence and higher overall survival. Conclusion: The findings revealed that patients with HER2 2+ had better outcome in comparison to the patients with HER2 0 and HER2 1+. Furthermore, the results showed that many patients with HER2 2+ expression were not basal-like and had good prognosis amongst TNBC patients.

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Highlights Fine-grained and sensitive dynamic subnetwork redundancy metric for disease studies. New connectedness metrics measure network robustness and resilience. Expanded current graph theory metrics to network redundancy in addition to efficiency. Increased redundancy of the subcortical-cerebellum network could be an early sign of AD. Decreased redundancy of the medial frontal network could indicate depression.