  Graph convolutional learning has led to many exciting discoveries in diverse
areas. However, in some applications, traditional graphs are insufficient to
capture the structure and intricacies of the data. In such scenarios,
multigraphs arise naturally as discrete structures in which complex dynamics
can be embedded. In this paper, we develop convolutional information processing
on multigraphs and introduce convolutional multigraph neural networks (MGNNs).
To capture the complex dynamics of information diffusion within and across each
of the multigraph's classes of edges, we formalize a convolutional signal
processing model, defining the notions of signals, filtering, and frequency
representations on multigraphs. Leveraging this model, we develop a multigraph
learning architecture, including a sampling procedure to reduce computational
complexity. The introduced architecture is applied towards optimal wireless
resource allocation and a hate speech localization task, offering improved
performance over traditional graph neural networks.
