With the recent advances in graph neural networks, there is a rising number of studies on graph-based multi-label classification with the consideration of object dependencies within visual data. Nevertheless, graph representations can become indistinguishable due to the complex nature of label relationships. We propose a multi-label image classification framework based on graph transformer networks to fully exploit inter-label interactions. The paper presents a modular learning scheme to enhance the classification performance by segregating the computational graph into multiple sub-graphs based on modularity. The proposed approach, named Modular Graph Transformer Networks (MGTN), is capable of employing multiple backbones for better information propagation over different sub-graphs guided by graph transformers and convolutions. We validate our framework on MS-COCO and Fashion550K datasets to demonstrate improvements for multi-label image classification. The source code is available at https://github.com/ReML-AI/MGTN.