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Graph and hypergraph representation learning has attracted increasingattention from various research fields. Despite the decent performance andfruitful applications of Graph Neural Networks (GNNs), Hypergraph NeuralNetworks (HGNNs), and their well-designed variants, on some commonly usedbenchmark graphs and hypergraphs, they are outperformed by even a simpleMulti-Layer Perceptron. This observation motivates a reexamination of thedesign paradigm of the current GNNs and HGNNs and poses challenges ofextracting graph features effectively. In this work, a universal featureencoder for both graph and hypergraph representation learning is designed,called UniG-Encoder. The architecture starts with a forward transformation ofthe topological relationships of connected nodes into edge or hyperedgefeatures via a normalized projection matrix. The resulting edge/hyperedgefeatures, together with the original node features, are fed into a neuralnetwork. The encoded node embeddings are then derived from the reversedtransformation, described by the transpose of the projection matrix, of thenetwork's output, which can be further used for tasks such as nodeclassification. The proposed architecture, in contrast to the traditionalspectral-based and/or message passing approaches, simultaneously andcomprehensively exploits the node features and graph/hypergraph topologies inan efficient and unified manner, covering both heterophilic and homophilicgraphs. The designed projection matrix, encoding the graph features, isintuitive and interpretable. Extensive experiments are conducted anddemonstrate the superior performance of the proposed framework on twelverepresentative hypergraph datasets and six real-world graph datasets, comparedto the state-of-the-art methods. Our implementation is available online athttps://github.com/MinhZou/UniG-Encoder.

UniG-Encoder: A Universal Feature Encoder for Graph and Hypergraph Node Classification