You CAN batch train GCNs (or some of them are very amenable to that) some of the most scalable GCNs rely on something like GraphSAGE convolution which doesn’t require the whole graph laplacian for updates (this approach is used by Wikipedia, Uber, Pinterest) to train highly scalable GCNs). Other convolutional operators like GAT also can be batch trained.

You can use the Python package PyTorch-Geometric documentation as a jumping off point for reading about practical graph sub sampling.