Technical Report of Mixing Local Patterns

Graph neural networks (GNNs) have shown remarkable performance on homophilic graph data while being far less impressive when handling non-homophilic graph data due to the inherent low-pass filtering property of GNNs. In the face of analyzing complex real-world graphs with different homophily properties, the latent mixed local structural patterns in graphs should not be neglected. Therefore, the two questions, i.e., (\textbf{Q1}) and (\textbf{Q2}) as motioned above, should be well considered on the way to implementing a more generic GNN. For this purpose, we attempt to get deeper insights into them from two points, respectively, \textbf{(A1): Randomness of local patterns}, and \textbf{(A2): Aggregability of near-neighbors}.