The research team proposed a generative model called Embedded Graph Flow (EGF) aimed at solving the problem of classifying graph structures. This model uses a permutation-isomorphic graph transformer to transfer Gaussian noise to the continuous embedded endpoints of nodes and unordered edge categories, and maps back to discrete graph categories through a terminal reader. In molecular generation benchmarks, EGF performed excellently: on the QM9 dataset, its Fréchet ChemNet Distance (FCD) was 0.150, significantly better than the classification diffusion baseline DiGress (0.717) and the bridge-based baseline GruM (0.812), achieving the best results in all four metrics. Additionally, when applied to the ZINC250k dataset, EGF maintained the lowest maximum mean difference (MMD) with the neighborhood subgraph pairwise distance kernel (NSPDK), indicating its high consistency with the local substructures of reference molecules. The relevant code has been publicly released on the GitHub repository.