Measuring Spatial Correspondence among Network Paths

Abstract

Measuring the spatial correspondence among geographic features is an important component of many analyses such as those seeking to identify similar or dissimilar features, explore the extent to which change has taken place, and explain the processes influencing spatial change. In networked systems, the paths providing connectivity between pairs of nodes are often the geographic features among which spatial correspondence is to be assessed. That is, given a set of paths between a pair of nodes, the extent to which they share portions of the network and spatially deviate from one another can provide insight on the factors underlying the use of a system. While methods for measuring the spatial correspondence among specific types of network paths have been devised, this article proposes a methodology for measuring the spatial correspondence among the topology of network paths of any type, including those involving redundant use of network space. By basing comparisons upon the topologic relationships among the paths, the proposed approach better accounts for average spatial deviation as well as the asymmetric spatial relationship between pairs of paths, enabling greater stability and consistency in the analysis of their spatial characteristics. The developed methodology is applied to evaluate variability in spatial correspondence among a set of network paths to demonstrate its utility.