Small-world characteristics in geographic, epidemic, and virtual spaces : a comparative study

This dissertation focuses on a comparative study of small-world characteristics in geographical, epidemic, and virtual spaces. Small-world network is the major component of the ??????new science of networks?????? that emerged recently in research related to complex networks. It has shown a great potential to model the complex networks encountered in geographical studies. This dissertation, in an attempt to understand the emergence of small-world phenomenon in spatial networks, has investigated the smallworld properties in aforementioned three spaces. Specifically, this dissertation has studied roadway transportation networks at national, metropolitan, and intra-city scales via network autocorrelation methods to investigate the distance effect on the emergence of small-world properties. This dissertation also investigated the effect of small-world network properties on the epidemic diffusion and different control strategies through agent-based simulation on social networks. The ASLevel Internet in the contiguous U.S. has been studied in its relation between local and global connections, and its correspondence with small-world characteristics. Through theoretical simulations and empirical studies on spatial networks, this dissertation has contributed to network science with a new method ?????? network autocorrelation, and better understanding from the perspective of the relation between local and global connections and the distance effect in networks. A small-world phenomenon results from the interplay between the dynamics occurring on networks and the structure of networks; when the influencing distance of the dynamics reaches to the threshold of the network, the network will logically emerge as a small-world network. With the aid of numerical simulation a small-world network has a large number of local connections and a small number of global links. It is also found that the epidemics will take shorter time period to reach largest size on a small-world network and only particular control strategy, such as targeted control strategy, will be effective on smallworld networks. This dissertation bridges the gap between new science of networks and the network study in geography. It potentially contributes to GIScience with new modeling strategy for representing, analyzing, and modeling complexity in hazards prevention, landscape ecology, and sustainability science from a network-centric perspective.