  Graph Neural Networks (GNNs) have proven to be highly effective for node
classification tasks across diverse graph structural patterns. Traditionally,
GNNs employ a uniform global filter, typically a low-pass filter for homophilic
graphs and a high-pass filter for heterophilic graphs. However, real-world
graphs often exhibit a complex mix of homophilic and heterophilic patterns,
rendering a single global filter approach suboptimal. In this work, we
theoretically demonstrate that a global filter optimized for one pattern can
adversely affect performance on nodes with differing patterns. To address this,
we introduce a novel GNN framework Node-MoE that utilizes a mixture of experts
to adaptively select the appropriate filters for different nodes. Extensive
experiments demonstrate the effectiveness of Node-MoE on both homophilic and
heterophilic graphs.
