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This paper aims at studying the sample complexity of graph convolutionalnetworks (GCNs), by providing tight upper bounds of Rademacher complexity forGCN models with a single hidden layer. Under regularity conditions, thesesderived complexity bounds explicitly depend on the largest eigenvalue of graphconvolution filter and the degree distribution of the graph. Again, we providea lower bound of Rademacher complexity for GCNs to show optimality of ourderived upper bounds. Taking two commonly used examples as representatives, wediscuss the implications of our results in designing graph convolution filtersan graph distribution.

Generalization bounds for graph convolutional neural networks via Rademacher complexity