  Many irregular domains such as social networks, financial transactions,
neuron connections, and natural language constructs are represented using graph
structures. In recent years, a variety of graph neural networks (GNNs) have
been successfully applied for representation learning and prediction on such
graphs. In many of the real-world applications, the underlying graph changes
over time, however, most of the existing GNNs are inadequate for handling such
dynamic graphs. In this paper we propose a novel technique for learning
embeddings of dynamic graphs using a tensor algebra framework. Our method
extends the popular graph convolutional network (GCN) for learning
representations of dynamic graphs using the recently proposed tensor M-product
technique. Theoretical results presented establish a connection between the
proposed tensor approach and spectral convolution of tensors. The proposed
method TM-GCN is consistent with the Message Passing Neural Network (MPNN)
framework, accounting for both spatial and temporal message passing. Numerical
experiments on real-world datasets demonstrate the performance of the proposed
method for edge classification and link prediction tasks on dynamic graphs. We
also consider an application related to the COVID-19 pandemic, and show how our
method can be used for early detection of infected individuals from contact
tracing data.
