Predicting the critical temperature ($T_c$) of superconducting materials is central to the search for new superconductors. Conventional machine learning models depend on handcrafted descriptors, while existing graph neural networks do not jointly exploit superconducting category information and physicochemical statistics. We introduce the Hierarchical Graph $T_c$ Network (HGTC-Net), a joint classification-regression framework for $T_c$ prediction. Crystal structures from the 3DSC database are converted into graph representations whose node and edge features encode local atomic environments and interatomic interactions. An HSC-XGB module performs hierarchical superconducting classification, including binary identification and family recognition. The resulting category probabilities are injected into the PriorGNN regression model through a gating mechanism that guides graph representation learning and $T_c$ prediction. The model attains coefficients of determination $R^2=0.9065$ and 0.8809 on the training and test sets, respectively. The framework is further applied to 84 461 candidate structures from the GNoME database for external screening of previously unseen compounds. HGTC-Net therefore provides a route for screening high-$T_c$ superconductors.

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• Superconductivity
• Superconductors
• Data mining