DualGCN: A Convolutional Network for Anomaly Detection in Directed Graphs Based on Symmetrized and Skew-Symmetrized Laplacians

Graph machine learning techniques and notably graph neural networks (GNNs) have seen a surge in popularity due to the suitability of graphs for being the underlying data structure in a multitude of applications. Spectral graph convolutional networks (GCNs), however, seem to encounter shortfalls when it comes to directed graphs. The root cause lies in the asymmetric nature of the adjacency matrices and of the resulting Laplacians of such graphs; being ill-behaved with respect to the spectral theory. In this paper, we attempt to overcome this limitation through DualGCN: a spectral GCN approach based on the symmetrized and skew-symmetrized Laplacian matrices. To test the proposed method, we undertake the anomaly detection problem for graph-structured data and obtain better results than with other approaches.