The Properties of Topological Network Connectivity Measures and Their Application to US Urban Freeway Networks

摘要

The mathematical concepts of graph theory were introduced into geography in the early 1960s, providing a means of conceptualizing transport networks as made up of nodes and links. Among the contributions were several measures of topological network connectivity known as alpha (alpha), beta (beta), and gamma (gamma). These ratio measures identified the level of connectivity present in a network. These measures attracted considerable attention before fading from view, although they have recently returned to prominence in several applications. Despite this renewed attention, the basic mathematical properties of these measures remain largely unexamined. This research investigates the properties of these three simple ratio measures and explores values and properties that might be typical in urban freeway networks. Although simple correlation reveals little relationship between connectivity and freeway structure, they can be used to identify several groups of freeway networks as well as identifying important details about the use and interpretation of these measures. It is likely that these simple measures will continue to be applied to new situations, and this article provides some guidelines for those applications.