Parallel graph-oriented applications expressed in the Bulk-Synchronous Parallel (BSP) and Token Dataflow compute models generate highly-structured communication workloads from messages propagating along graph edges. We can statially expose this structure to traffic compilers and optimization tools to reshape and reduce traffic for higher performance (or lower area, lower energy, lower cost). Such offline traffic optimization eliminates the need for complex, runtime NoC hardware and enables lightweight, scalable NoCs. We perform load balancing, placement, fanout routing, and fine-grained synchronization to optimize our workloads for large networks up to 2025 parallel elements for BSP model and 25 parallel elements for Token Dataflow. This allows us to demonstrate speedups between 1.2× and 22× (3.5× mean), area reductions (number of Processing Elements) between 3× and 15× (9× mean) and dynamic energy savings between 2× and 3.5× (2.7× mean) over a range of real-world graph applications in the BSP compute model. We deliver speedups of 0.5–13× (geomean 3.6×) for Sparse Direct Matrix Solve (Token Dataflow compute model) applied to a range of sparse matrices when using a high-quality placement algorithm. We expect such traffic optimization tools and techniques to become an essential part of the NoC application-mapping flow.