Statistical details of the datasets.

The identification of cancer driver genes (CDGs) poses challenges due to the intricate interdependencies among genes and the influence of measurement errors and noise. We propose a novel energy-constrained diffusion (ECD)-based model for identifying CDGs, termed ECD-CDGI. This model is the first to design an ECD-Attention encoder by combining the ECD technique with an attention mechanism. ECD-Attention encoder excels at generating robust gene representations that reveal the complex interdependencies among genes while reducing the impact of data noise. We concatenate topological embedding extracted from gene-gene networks through graph transformers to these gene representations. We conduct extensive experiments across three testing scenarios. Extensive experiments show that the ECD-CDGI model possesses the ability to not only be proficient in identifying known CDGs but also efficiently uncover unknown potential CDGs. Furthermore, compared to the GNN-based approach, the ECD-CDGI model exhibits fewer constraints by existing gene-gene networks, thereby enhancing its capability to identify CDGs. Additionally, ECD-CDGI is open-source and freely available. We have also launched the model as a complimentary online tool specifically crafted to expedite research efforts focused on CDGs identification.