The development of graph neural networks has been driven by the widespread area of applications where graphs are naturally fit and by the advances in making solutions scalable. When it comes to spectral graph convolutional networks (GCNs), directed graphs suffer from the asymmetric nature of their Laplacian matrices. For such graphs, there is no natural extension of the spectral graph theory well-established for their undirected analogues with inherent symmetric matrices. In this paper, we propose i-DGCN: a spectral GCN approach addressing directed graphs by means of a novel symmetric Laplacian matrix constructed using a quantification of the interaction between the nodes. In order to assess i-DGCN, we undertake two tasks: anomaly detection for graph-structured data (unsupervised) and graph link existence prediction (supervised). Then, we compare the results with other Laplacian alternatives for directed graphs.

Graphs can model various systems, activities, or interactions. As a consequence, the ability to detect anomalies in graph-structured data is needed in many scenarios. This paper introduces Community-Augmented Local-Link Intensity (CALLI), an algorithm for quantifying the abnormality extent of nodes in a weighted digraph. Experiments are performed on both synthetically generated and real graphs modeling financial transactions. Throughout the tests, CALLI is directly used as the sole decision-making anomaly score, but also as a feature in a conventional outlier detection approach.