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Heterophily has been considered as an issue that hurts the performance ofGraph Neural Networks (GNNs). To address this issue, some existing work uses agraph-level weighted fusion of the information of multi-hop neighbors toinclude more nodes with homophily. However, the heterophily might differ amongnodes, which requires to consider the local topology. Motivated by it, wepropose to use the local similarity (LocalSim) to learn node-level weightedfusion, which can also serve as a plug-and-play module. For better fusion, wepropose a novel and efficient Initial Residual Difference Connection (IRDC) toextract more informative multi-hop information. Moreover, we providetheoretical analysis on the effectiveness of LocalSim representing nodehomophily on synthetic graphs. Extensive evaluations over real benchmarkdatasets show that our proposed method, namely Local Similarity Graph NeuralNetwork (LSGNN), can offer comparable or superior state-of-the-art performanceon both homophilic and heterophilic graphs. Meanwhile, the plug-and-play modelcan significantly boost the performance of existing GNNs. Our code is providedat https://github.com/draym28/LSGNN.

LSGNN: Towards General Graph Neural Network in Node Classification by Local Similarity