  Graph Neural Networks (GNNs) show strong expressive power on graph data
mining, by aggregating information from neighbors and using the integrated
representation in the downstream tasks. The same aggregation methods and
parameters for each node in a graph are used to enable the GNNs to utilize the
homophily relational data. However, not all graphs are homophilic, even in the
same graph, the distributions may vary significantly. Using the same
convolution over all nodes may lead to the ignorance of various graph patterns.
Furthermore, many existing GNNs integrate node features and structure
identically, which ignores the distributions of nodes and further limits the
expressive power of GNNs. To solve these problems, we propose Meta Weight Graph
Neural Network (MWGNN) to adaptively construct graph convolution layers for
different nodes. First, we model the Node Local Distribution (NLD) from node
feature, topological structure and positional identity aspects with the
Meta-Weight. Then, based on the Meta-Weight, we generate the adaptive graph
convolutions to perform a node-specific weighted aggregation and boost the node
representations. Finally, we design extensive experiments on real-world and
synthetic benchmarks to evaluate the effectiveness of MWGNN. These experiments
show the excellent expressive power of MWGNN in dealing with graph data with
various distributions.
