The identification of stage-related driving factors in breast carcinoma based on network smoothing and gravity model

Breast carcinoma (BRCA) is a leading cause of mortality in women worldwide. Understanding the driving factors behind BRCA initiation, progression, and evolution is crucial. This study proposes a novel method to identify stage-related driving factors in BRCA. By utilizing stage-specific functional interaction networks, the multi-omics features and PPI were integrated. A novel rumor-mongering model is introduced to smooth the stage-specific networks and the gravity model is used to balance gene interactions. The top 100 gravity interactions are identified as driving factors. Through biomolecular and enrichment analyses, these driving factors are shown to play a crucial role in BRCA progression. Furthermore, a hybrid hierarchical evolution network illustrates the stage-evolutionary role of driving factors, while a biological functional evolution network demonstrates functional changes in BRCA progression. The proposed method exhibits superior enrichment performance, particularly within targeted pathways, providing valuable insights into the underlying mechanisms of BRCA.