Increasing use of "hubs" as switching centers through which large volumes of traffic are channelled has transformed the character of many transportation and communications networks. Scholars in geography, regional science, operations research, and related fields have recently given more attention on the role of hubs in circulation networks, but most studies conducted to date have focused on the characteristics of individual nodes rather than on the entire network. This research project will build on work already completed by the investigator that enhances theoretical models of spatial interaction. These improvements will determine the number and location of hubs that would best serve a network and the best routing of flows through the network. The research will combine extension of mathematical models to accommodate additional factors that more accurately reflect actual conditions within which networks function, the development of heuristic procedures for better determining solutions for such complex models, and the analyses of graphic representations of networks to measure the connectivity and efficiency of alternative networks. The project will set the stage for empirical analyses of hub systems in a variety of different types of networks. This project will significantly advance theoretical understandings of the roles of hubs within circulation systems by more realistically representing network configurations and operations and by assessing hub operations from perspectives of overall network efficiency. Previous work by the investigator along this line of inquiry already has been a catalyst for new studies by other scholars examining spatial interaction and other locational factors; this project will continue to foster that kind of advancement. This research ultimately will also yield practical rewards, by providing an improved basis for assessing the operation of real circulation networks and by encouraging development of new procedures for determining optimal configurations of new networks.