Dragonflies are recent network designs that are one of the most promising topologies for the Exascale effort due to their scalability and cost. While being able to achieve very high throughput under random uniform all-to-all traffic, this type of network can experience significant performance degradation for other common high performance computing workloads such as stencil (multi-dimensional nearest neighbor) patterns. Often, the lack of peak performance is caused by an insufficient understanding of the interaction between the workload and the network, and an insufficient understanding of how application specific task-to-node mapping strategies can serve as optimization vehicles. To address these issues, we propose a theoretical performance analysis framework that takes as inputs a network specification and a traffic demand matrix characterizing an arbitrary workload and is able to predict where bottlenecks will occur in the network and what their impact will be on the effective sustainable injection bandwidth. We then focus our analysis on a specific high-interest communication pattern, the multi-dimensional Cartesian nearest neighbor exchange, and provide analytic bounds (owing to bottlenecks in the remote links of the Dragonfly) on its expected performance across a multitude of possible mapping strategies. Finally, using a comprehensive set of simulations results, we validate the correctness of the theoretical approach and in the process address some misconceptions regarding Dragonfly network behavior and evaluation, (such as the choice of throughput maximization over workload completion time minimization as optimization objective) and the question of whether the standard notion of Dragonfly balance can be extended to workloads other than uniform random traffic. Copyright © 2014 ACM.