Finite-Size Convergence Bound of Graph Convolutional Networks by Graphon Analysis

Graph Convolutional Networks (GCNs) prevail in the analysis of network-structured data, but how the graph size affects the performance is not fully understood. As the limit of graphs, the graphon tool has been widely adopted to analyze the convergence of GCN in the literature. However, current results either apply to fully connected graphs or require sufficiently large graph sizes, which do not provide a theoretical guarantee in finite-size GCNs. In this paper, we provide a finite-size bound for the convergence properties of GCNs that imposes no constraints on downstream tasks and applies to random edge graphs. Furthermore, we validate the theoretical bound through experiments.