Centrality Measures on Graphs

In studying networks (be they social networks, road networks, communication networks, etc.) one is often interested in measuring the relative importance of various nodes and arcs and identifying the most important ones. In the context of road networks, one measure of importance (or centrality) is the amount of traffic that flows through a given road or intersection. The goal of this project is to determine, under various conditions, the structures of highly centralized and/or highly decentralized networks and to study means by which given networks could be made more or less centralized. This would allow one, for example, to anticipate busy/congested routes and to identify possible links that would improve the situation. The results of the study may be applied in Qatar in order to alleviate the strains that growing demands might place on its various road and communication networks.