  In this paper, we propose a simple yet effective graph neural network for
directed graphs (digraph) based on the classic Singular Value Decomposition
(SVD), named SVD-GCN. The new graph neural network is built upon the graph
SVD-framelet to better decompose graph signals on the SVD ``frequency'' bands.
Further the new framelet SVD-GCN is also scaled up for larger scale graphs via
using Chebyshev polynomial approximation. Through empirical experiments
conducted on several node classification datasets, we have found that SVD-GCN
has remarkable improvements in a variety of graph node learning tasks and it
outperforms GCN and many other state-of-the-art graph neural networks for
digraphs. Moreover, we empirically demonstate that the SVD-GCN has great
denoising capability and robustness to high level graph data attacks. The
theoretical and experimental results prove that the SVD-GCN is effective on a
variant of graph datasets, meanwhile maintaining stable and even better
performance than the state-of-the-arts.
