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Graph neural networks (GNNs) are efficient techniques for learning graph representations and have shown remarkable success in tackling diverse graph-related tasks. However, in the context of the neighborhood aggregation paradigm, conventional GNNs have limited capabilities in capturing the higher order structures and topological semantics of graphs. Researchers have attempted to overcome this limitation by designing new GNNs that explore the impacts of motifs to capture potentially higher order graph information. However, existing motif-based GNNs often ignore lower order connectivity patterns such as nodes and edges, which leads to poor representation of sparse networks. To address these limitations, we propose an innovative approach. First, we design convolution kernels on both motif-based and simple graphs. Second, we introduce a multilevel graph convolution framework for extracting higher …