  Due to the homophily assumption in graph convolution networks (GNNs), a
common consensus in the graph node classification task is that GNNs perform
well on homophilic graphs but may fail on heterophilic graphs with many
inter-class edges. However, the previous inter-class edges perspective and
related homo-ratio metrics cannot well explain the GNNs performance under some
heterophilic datasets, which implies that not all the inter-class edges are
harmful to GNNs. In this work, we propose a new metric based on von Neumann
entropy to re-examine the heterophily problem of GNNs and investigate the
feature aggregation of inter-class edges from an entire neighbor identifiable
perspective. Moreover, we propose a simple yet effective Conv-Agnostic GNN
framework (CAGNNs) to enhance the performance of most GNNs on heterophily
datasets by learning the neighbor effect for each node. Specifically, we first
decouple the feature of each node into the discriminative feature for
downstream tasks and the aggregation feature for graph convolution. Then, we
propose a shared mixer module to adaptively evaluate the neighbor effect of
each node to incorporate the neighbor information. The proposed framework can
be regarded as a plug-in component and is compatible with most GNNs. The
experimental results over nine well-known benchmark datasets indicate that our
framework can significantly improve performance, especially for the heterophily
graphs. The average performance gain is 9.81%, 25.81%, and 20.61% compared with
GIN, GAT, and GCN, respectively. Extensive ablation studies and robustness
analysis further verify the effectiveness, robustness, and interpretability of
our framework. Code is available at https://github.com/JC-202/CAGNN.
