Topology-based proximities in spatial systems

This paper introduces several topology-based measures that characterise proximity relationships between regions in a spatial system. These measures are derived from a relative adjacency operator that is computed from the dual graph of a spatial system. The operator is flexible as the respective importance of neighbouring and outlying regions can be parameterised. Given a reference region in a spatial system, we also show how the relative adjacency supports the analysis of the relative distribution of other regions, and how these regions are clustered with respect to that reference region. Extensions of the relative adjacency integrate additional spatial and thematic criteria. The properties of the relative adjacency are illustrated by means of reference examples and a case study.