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Many irregular domains such as social networks, financial transactions,neuron connections, and natural language constructs are represented using graphstructures. In recent years, a variety of graph neural networks (GNNs) havebeen successfully applied for representation learning and prediction on suchgraphs. In many of the real-world applications, the underlying graph changesover time, however, most of the existing GNNs are inadequate for handling suchdynamic graphs. In this paper we propose a novel technique for learningembeddings of dynamic graphs using a tensor algebra framework. Our methodextends the popular graph convolutional network (GCN) for learningrepresentations of dynamic graphs using the recently proposed tensor M-producttechnique. Theoretical results presented establish a connection between theproposed tensor approach and spectral convolution of tensors. The proposedmethod TM-GCN is consistent with the Message Passing Neural Network (MPNN)framework, accounting for both spatial and temporal message passing. Numericalexperiments on real-world datasets demonstrate the performance of the proposedmethod for edge classification and link prediction tasks on dynamic graphs. Wealso consider an application related to the COVID-19 pandemic, and show how ourmethod can be used for early detection of infected individuals from contacttracing data.

Dynamic Graph Convolutional Networks Using the Tensor M-Product