According to the data from our clinical cohort, the results of the ROC analysis showed that values of the vertex and edge panels were significantly negatively associated with overall survival similar to AFP (all P < 0.001; Figure 5a–c), while the vertex and the edge panels had better performances in HCC prognosis than individual genes (Supplementary Figure S4) and gene pairs (Supplementary Figure S5). This evidence concerns the gene AFP and hepatocellular carcinoma.