  Graph Neural Networks (GNNs) are information processing architectures for
signals supported on graphs. They are presented here as generalizations of
convolutional neural networks (CNNs) in which individual layers contain banks
of graph convolutional filters instead of banks of classical convolutional
filters. Otherwise, GNNs operate as CNNs. Filters are composed with pointwise
nonlinearities and stacked in layers. It is shown that GNN architectures
exhibit equivariance to permutation and stability to graph deformations. These
properties help explain the good performance of GNNs that can be observed
empirically. It is also shown that if graphs converge to a limit object, a
graphon, GNNs converge to a corresponding limit object, a graphon neural
network. This convergence justifies the transferability of GNNs across networks
with different number of nodes. Concepts are illustrated by the application of
GNNs to recommendation systems, decentralized collaborative control, and
wireless communication networks.
