Intersections are among the most hazardous roadway spaces due to the complex and conflicting road users’ movements. Spatio-temporal modeling of conflict risks among road users can help to identify strategies to mitigate the exacerbation of safety risks and restore hazardous conditions to normal traffic situations. This paper proposes the 'Conflict Risk Graph' as a novel concept to infer real-time conflict risks at intersections at a fine-grained level by mapping conflict-prone locations to nodes within a network characterized by specific topological structures. A significant contribution of this work is the development of a Transformer-based Graph Convolutional Network (Trans-GCN), a model that synergistically combines the Transformer's proficiency in capturing global dependence with the GCN's ability to learn local correlations. The Trans-GCN adeptly models the complex evolution patterns of conflict risks at intersections. The evaluation in this paper against five common state-of-the-art deep learning approaches demonstrates the superior performance of the Trans-GCN in conflict risk inference and adaptability to node changes. Furthermore, extensive experiments with different node configurations reveal a correlation between node setup and model performance, showing that higher spatio-temporal resolution decreases inference accuracy. This insight informs the selection of an optimal node configuration that balances the detailed capture of spatio-temporal dynamics with modeling accuracy, enabling ideal conflict risk inferences at intersections. Ultimately, this work offers significant insights for the enhancement of proactive traffic safety management and the advancement of intelligent traffic systems.