Operational reliability assessment (ORA), which evaluates the risk level of power systems, is hindered by accumulated computational burdens and thus cannot meet the demands of real-time assessment. Recently, data-driven methods with fast calculation speeds have emerged as a research focus for online ORA. However, the diverse contingencies of transformers, power lines, and other components introduce numerous topologies, posing significant challenges to the learning capabilities of neural networks. To this end, this paper proposes a multi-kernel collaborative graph convolution neural network (GCNN) for ORA considering varying topologies. Specifically, a physics law-informed graph convolution kernel derived from the Gaussian-Seidel iteration is introduced. It effectively aggregates node features across different topologies. By integrating additional advanced graph convolution kernels with a novel self-attention mechanism, the multi-kernel collaborative GCNN is constructed, which enables the extraction of diverse features and the construction of representative node feature vectors, thereby facilitating high-precision reliability assessments. Furthermore, to enhance the robustness of multi-kernel collaborative GCNN, the inherent pattern of the load-shedding model is analyzed and utilized to design a specialized supervised loss function, which allows the neural network to explore a broader feature space. Compared with the existing data-driven methods, the multi-kernel collaborative GCNN, combined with supervised exploration, can accommodate a wider range of contingencies and achieve superior assessment accuracy.