Graph neural networks for network analysis

With an increasing number of applications where data can be represented as graphs, graph neural networks (GNNs) are a useful tool to apply deep learning to graph data. Signed and directed networks are important forms of networks that are linked to many real-world problems, such as ranking from pairwise comparisons, and angular synchronization. In this report, we propose two spatial GNN methods for node clustering in signed and directed networks, a spectral GNN method for signed directed networks on both node clustering and link prediction, and two GNN methods for specific applications in ranking as well as angular synchronization. The methods are end-to-end in combining embedding generation and prediction without an intermediate step. Experimental results on various data sets, including several synthetic stochastic block models, random graph outlier models, and real-world data sets at different scales, demonstrate that our proposed methods can achieve satisfactory performance, for a wide range of noise and sparsity levels. The introduced models also complement existing methods through the possibility of including exogenous information, in the form of node-level features or labels. Their contribution not only aid the analysis of data which are represented by networks, but also form a body of work which presents novel architectures and task-driven loss functions for GNNs to be used in network analysis