  Graph Convolutional Networks (GCNs) suffer from performance degradation when
models go deeper. However, earlier works only attributed the performance
degeneration to over-smoothing. In this paper, we conduct theoretical and
experimental analysis to explore the fundamental causes of performance
degradation in deep GCNs: over-smoothing and gradient vanishing have a mutually
reinforcing effect that causes the performance to deteriorate more quickly in
deep GCNs. On the other hand, existing anti-over-smoothing methods all perform
full convolutions up to the model depth. They could not well resist the
exponential convergence of over-smoothing due to model depth increasing. In
this work, we propose a simple yet effective plug-and-play module, Skipnode, to
overcome the performance degradation of deep GCNs. It samples graph nodes in
each convolutional layer to skip the convolution operation. In this way, both
over-smoothing and gradient vanishing can be effectively suppressed since (1)
not all nodes'features propagate through full layers and, (2) the gradient can
be directly passed back through ``skipped'' nodes. We provide both theoretical
analysis and empirical evaluation to demonstrate the efficacy of Skipnode and
its superiority over SOTA baselines.
