  This paper aims at studying the sample complexity of graph convolutional
networks (GCNs), by providing tight upper bounds of Rademacher complexity for
GCN models with a single hidden layer. Under regularity conditions, theses
derived complexity bounds explicitly depend on the largest eigenvalue of graph
convolution filter and the degree distribution of the graph. Again, we provide
a lower bound of Rademacher complexity for GCNs to show optimality of our
derived upper bounds. Taking two commonly used examples as representatives, we
discuss the implications of our results in designing graph convolution filters
an graph distribution.
