  Recent graph neural networks (GNN) has achieved remarkable performance in
node representation learning. One key factor of GNN's success is the
\emph{smoothness} property on node representations. Despite this, most GNN
models are fragile to the perturbations on graph inputs and could learn
unreliable node representations. In this paper, we study how to learn node
representations against perturbations in GNN. Specifically, we consider that a
node representation should remain stable under slight perturbations on the
input, and node representations from different structures should be
identifiable, which two are termed as the \emph{stability} and
\emph{identifiability} on node representations, respectively. To this end, we
propose a novel model called Stability-Identifiability GNN Against
Perturbations (SIGNNAP) that learns reliable node representations in an
unsupervised manner. SIGNNAP formalizes the \emph{stability} and
\emph{identifiability} by a contrastive objective and preserves the
\emph{smoothness} with existing GNN backbones. The proposed method is a generic
framework that can be equipped with many other backbone models (e.g. GCN,
GraphSage and GAT). Extensive experiments on six benchmarks under both
transductive and inductive learning setups of node classification demonstrate
the effectiveness of our method. Codes and data are available
online:~\url{https://github.com/xuChenSJTU/SIGNNAP-master-online}
