The Transferability of Downsampling Sparse Graph Convolutional Networks

In this paper, we propose a large-scale sparse graph downsampling method based on a sparse random graph model, which allows for the adjustment of different sparsity levels. We combine sparsity and topological similarity: the sparse graph model reduces the node connection probability as the graph size increases, while the downsampling method preserves a specific topological connection pattern during this change. Based on the downsampling method, we derive a theoretical transferability bound about downsampling sparse graph convolutional networks (GCNs), that higher sampling rates, greater average degree expectations, and smaller initial graph sizes lead to better downsampling transferability performance.