INDIRECT CONNECTIVITY AND HIERARCHIES OF URBAN DOMINANCE.

Activities exert control in urban systems by facilitating the direct and indirect flows of other activities. If a matrix of direct flows is raised to successive powers, the power at which each cell first becomes positive represents the minimum number of direct and indirect steps linking activities. From a matrix of minimum steps an average number of steps can be computed for each activity. To find an activity's degree of control its direct flows are removed from the system and this average number of steps is recomputed for activities remaining. The mean absolute difference between these averages in the original and reduced systems reflects the changed connectivity faced by the flows of remaining activities. The control of activities can be ranked using this mean. Applying this technique to India's system of airline flows identified an urban hierarchy with for levels of connectivity: national, regional, subregional and route endings. [ABSTRACT FROM AUTHOR]