  Graph Neural Networks (GNNs) have become a prominent approach to machine
learning with graphs and have been increasingly applied in a multitude of
domains. Nevertheless, since most existing GNN models are based on flat
message-passing mechanisms, two limitations need to be tackled: (i) they are
costly in encoding long-range information spanning the graph structure; (ii)
they are failing to encode features in the high-order neighbourhood in the
graphs as they only perform information aggregation across the observed edges
in the original graph. To deal with these two issues, we propose a novel
Hierarchical Message-passing Graph Neural Networks framework. The key idea is
generating a hierarchical structure that re-organises all nodes in a flat graph
into multi-level super graphs, along with innovative intra- and inter-level
propagation manners. The derived hierarchy creates shortcuts connecting
far-away nodes so that informative long-range interactions can be efficiently
accessed via message passing and incorporates meso- and macro-level semantics
into the learned node representations. We present the first model to implement
this framework, termed Hierarchical Community-aware Graph Neural Network
(HC-GNN), with the assistance of a hierarchical community detection algorithm.
The theoretical analysis illustrates HC-GNN's remarkable capacity in capturing
long-range information without introducing heavy additional computation
complexity. Empirical experiments conducted on 9 datasets under transductive,
inductive, and few-shot settings exhibit that HC-GNN can outperform
state-of-the-art GNN models in network analysis tasks, including node
classification, link prediction, and community detection. Moreover, the model
analysis further demonstrates HC-GNN's robustness facing graph sparsity and the
flexibility in incorporating different GNN encoders.
