  Graph convolution is a fundamental building block for many deep neural
networks on graph-structured data. In this paper, we introduce a simple, yet
very effective graph convolutional network with skip connections for
semi-supervised anomaly detection. The proposed layerwise propagation rule of
our model is theoretically motivated by the concept of implicit fairing in
geometry processing, and comprises a graph convolution module for aggregating
information from immediate node neighbors and a skip connection module for
combining layer-wise neighborhood representations. This propagation rule is
derived from the iterative solution of the implicit fairing equation via the
Jacobi method. In addition to capturing information from distant graph nodes
through skip connections between the network's layers, our approach exploits
both the graph structure and node features for learning discriminative node
representations. These skip connections are integrated by design in our
proposed network architecture. The effectiveness of our model is demonstrated
through extensive experiments on five benchmark datasets, achieving better or
comparable anomaly detection results against strong baseline methods. We also
demonstrate through an ablation study that skip connection helps improve the
model performance.
