Communication networks support a wide range of applications in multi-agent systems by solving core problems such as routing, scheduling, and resource allocation. In this thesis, we focus on data-driven routing and scheduling strategies using local information subject to constraints using Graph Neural Networks (GNNs). First, we study information routing in communication networks with constant channel conditions and formulate it as a constrained learning problem. We propose a novel State Augmentation strategy to achieve faster convergence and achieve decentralized implementation using GNNs. The state augmentation based optimization framework leverages graph convolutions to generate optimal routing decisions using only local information from the nearby neighbors and achieves competitive performance without the need for supervision or global knowledge. Second, we extend the framework to opportunistic routing in wireless networks, where we leverage the broadcast nature of wireless channels for dynamic relay node selection. We integrate state augmentation with GNN-based distributed optimization to learn efficient routing policies that maximize end-to-end throughput. The learned models can be generalized across varying network sizes and multiple flows which are very robust to network variations. Third, we design a real-time wireless ad-hoc network testbed to validate the proposed routing strategies under realistic channel conditions. Our evaluation demonstrates that the state augmentation combined GNN framework validates the simulational algorithms in terms of queue length stability while retaining stability and transferability properties without the requirement for retraining. Overall, this thesis presents a scalable and decentralized approach to intelligent routing and scheduling in multi-agent systems by bridging graph-based learning with network optimization, offering practical solutions for large-scale and dynamic communication systems.