Searching for 2D Spatial Network Holes

Abstract

Research involving different forms of networks, such as internet networks, social networks, and cellular networks, has increasingly become an important field of study. From this work, a variety of different scaling laws have been discovered. However, these aspatial laws, stemming from graph theory, often do not apply to spatial networks. When searching for network holes, results from graph theory frequently do not correlate with 2D spatial holes that enforce planarity. We present a general approach for finding holes in a 2D spatial network, and in particular for a network representing street centrelines of an area in Washington, D.C. This methodology involves finding graph holes that can be restricted to 2D spatial holes by examining topological relationships between network features. These spatial network holes gain significance as the number of edges encompassing the hole, and the length of these edges increase. For this reason, our approach is designed to classify these holes into different sets based on the number of edges found and the length of those edges. The results of this application provide valuable insights in the nature of the network, highlighting areas that we know from experience are poorly connected and thus suffer from low accessibility.