Paragraphs are an important class of document entities. We propose a new approach for paragraph recognition by spatial graph convolutional networks (GCN) applied on OCR text boxes. Two steps, namely line splitting and line clustering, are performed to extract paragraphs from the lines in OCR results. Each step uses a beta-skeleton graph constructed from bounding boxes, where the graph edges provide efficient support for graph convolution operations. With pure layout input features, the GCN model size is 3~4 orders of magnitude smaller compared to R-CNN based models, while achieving comparable or better accuracies on PubLayNet and other datasets. Furthermore, the GCN models show good generalization from synthetic training data to real-world images, and good adaptivity for variable document styles.