  Graph Neural Networks (GNNs) are recently proposed neural network structures
for the processing of graph-structured data. Due to their employed neighbor
aggregation strategy, existing GNNs focus on capturing node-level information
and neglect high-level information. Existing GNNs therefore suffer from
representational limitations caused by the Local Permutation Invariance (LPI)
problem. To overcome these limitations and enrich the features captured by
GNNs, we propose a novel GNN framework, referred to as the Two-level GNN
(TL-GNN). This merges subgraph-level information with node-level information.
Moreover, we provide a mathematical analysis of the LPI problem which
demonstrates that subgraph-level information is beneficial to overcoming the
problems associated with LPI. A subgraph counting method based on the dynamic
programming algorithm is also proposed, and this has time complexity is O(n^3),
n is the number of nodes of a graph. Experiments show that TL-GNN outperforms
existing GNNs and achieves state-of-the-art performance.
