This paper presents a driver-specific risk recognition framework for autonomous vehicles that can extract inter-vehicle interactions. This extraction is carried out for urban driving scenarios in a driver-cognitive manner to improve the recognition accuracy of risky scenes. First, clustering analysis is applied to the operation data of drivers for learning the subjective assessment of risky scenes of different drivers and generating the corresponding risk label for each scene. Second, the graph representation model (GRM) is adopted to unify and construct the features of dynamic vehicles, inter-vehicle interactions and static traffic markings in real driving scenes into graphs. The driver-specific risk label provides ground truth to capture the risk evaluation criteria of different drivers. In addition, the graph model represents multiple features of the driving scenes. Therefore, the proposed framework can learn the risk-evaluating pattern of driving scenes of different drivers and establish driver-specific risk identifiers. Last, the performance of the proposed framework is evaluated via experiments conducted using real-world urban driving datasets collected by multiple drivers. The results show that the risks and their levels in real driving environments can be accurately recognized by the proposed framework.