  Graph neural networks (GNNs) have recently received significant attention.
Learning node-wise message propagation in GNNs aims to set personalized
propagation steps for different nodes in the graph. Despite the success,
existing methods ignore node priority that can be reflected by node influence
and heterophily. In this paper, we propose a versatile framework PPro, which
can be integrated with most existing GNN models and aim to learn prioritized
node-wise message propagation in GNNs. Specifically, the framework consists of
three components: a backbone GNN model, a propagation controller to determine
the optimal propagation steps for nodes, and a weight controller to compute the
priority scores for nodes. We design a mutually enhanced mechanism to compute
node priority, optimal propagation step and label prediction. We also propose
an alternative optimization strategy to learn the parameters in the backbone
GNN model and two parametric controllers. We conduct extensive experiments to
compare our framework with other 11 state-of-the-art competitors on 8 benchmark
datasets. Experimental results show that our framework can lead to superior
performance in terms of propagation strategies and node representations.
