Abstract Graph Convolutional Networks (GCNs) are a subcategory of neural networks that can take a graph as input. They have been solicited lately due to their success and the ubiquity of data that can be represented as graphs. However, handling large graphs has been one of the main challenges for GCNs, along with the oversmoothing problem that can be caused by the depth or the large receptive field of GCNs. A lot of work has been done to address this problem with different approaches. A promising one is the consideration of the minibatch training paradigm and extending it to graph structured data by extracting subgraphs to be used as batches. Unlike the entries of a dataset of images that are independent from one another, the essence of a graph is its topology structure, hence the dependency between its nodes. Thus, the strategy of selecting subgraphs to form minibatches is a difficult task with a huge impact on the results of the training process. In this work, we propose a general framework for generating minibatches in an effective way that ensures a minimum loss in node interdependence information, preserves the original graph properties, and diversifies the samples for the GCN to better generalize afterwards. We test our training process on real world datasets with several well known GCN models and show the results improvement compared to existing methods. The source code and data are publicly available at https://gitlab.liris.cnrs.fr/hseba/sffs-gcn.