||Distributed software-defined networks (SDN), consisting of multiple inter-connected network domains, each managed by one SDN controller, is an emerging networking architecture that offers balanced centralized control and distributed operations. Under such networking paradigm, most existing works focus on designing sophisticated controller-synchronization strategies to improve joint controller-decision-making for interdomain routing. However, there is still a lack of fundamental understanding of how the performance of distributed SDN is related to network attributes, thus impossible to justify the necessity of complicated strategies. In this regard, we analyze and quantify the performance enhancement of distributed SDN architectures, influenced by intra-/inter-domain synchronization levels and network structural properties. Based on a generic weighted network model, we establish analytical methods for performance estimation under four synchronization scenarios with increasing synchronization cost. Moreover, two of these synchronization scenarios correspond to extreme cases, i.e., minimum/maximum synchronization, which are, therefore, capable of bounding the performance of distributed SDN with any given synchronization levels. Our theoretical results reveal how network performance is related to synchronization levels and inter-domain connections, the accuracy of which are confirmed by simulations based on both real and synthetic networks. To the best of our knowledge, this is the first work quantifying the performance of distributed SDN analytically, which provides fundamental guidance for future SDN protocol designs and performance estimation.