Before revision:  We design an expressive search space that focuses on a common and critical component of GNNs -- propagation model. Specifically, we search for propagation matrices and the connections between propagation steps. Our search space covers various graph types, e.g., homogeneous graphs, heterogeneous graphs, and can be naturally extended to higher-dimensional recommender systems and spatial-temporal data. We propose a sampling-based one-shot NAS algorithm to search for appropriate propagation patterns efficiently. Extensive experiments in three different scenarios are used to evaluate the proposed framework. We show that the performance of the models obtained by our framework is better than state-of-the-art GNN methods .
After revision:  We design an expressive search space in the form of a directed acyclic graph (DAG) to represent candidate meta graphs for a HIN, and we propose task-dependent type constraint to filter out those edge types along which message passing has no effect on the representations of nodes that are related to the downstream task. The size of the search space we define is huge, so we further propose a novel and efficient search algorithm to make the total search cost on a par with training a single GNN once. Compared with existing popular NAS algorithms, our proposed search algorithm improves the search efficiency. We conduct extensive experiments on different HINs and downstream tasks to evaluate our method, and experimental results show that our method can outperform state-of-the-art GNN methods .