Table 3 The results of the R_P and RMSE with standard deviation of the proposed models (GES_PPI and gnn_PPI)

0.6491 \(\pm\) 0.0108

1.1324 \(\pm\) 0.0114

0.7166 \(\pm\) 0.1022

1.6413 \(\pm\) 0.0840

0.6892 \(\pm\) 0.0126

1.5633 \(\pm\) 0.0143

0.5679 \(\pm\) 0.0221

1.7622 \(\pm\) 0.1421

0.7538 \(\pm\) 0.1097

2.1421 \(\pm\) 0.0988

0.6272 \(\pm\) 0.0441

1.2197 \(\pm\) 0.0308

0.6725 \(\pm\) 0.1320

1.6944 \(\pm\) 0.0806

0.6254 \(\pm\) 0.1052

1.5697 \(\pm\) 0.1231

0.5433 \(\pm\) 0.2597

1.7607 \(\pm\) 0.2080

0.7397 \(\pm\) 0.1956

2.1756 \(\pm\) 0.1427