Variable-Specific Classification of Zones, Pairs of Zones, and Clusters of a Spatial System via Modified Gravity Model

Abstract

Hierarchical structures include spatial systems (e.g., a continent), clusters of a spatial system (e.g., countries of a continent), zones of a cluster (e.g., states of a country), and so on. Variable-specific classification of the zones (X i ) of a cluster of zones (X) within a spatial system is the main focus of this paper. Variable-specific (e.g., GDP, population, trade, resources, economic activity etc) classification of zones is done by computing the levels of interaction between the ith and jth zones. Based on a heuristic argument, we proposed a modified gravity model for the computation of levels of interaction between the zones. This argument is based on the following two facts: (i) the level of interaction between the zones X i and X j , with masses mX i and mX j is direction-dependent, and (ii) the level of interactions between the zones X i and X j , with masses mX i and mX j , situated at strategically insignificant locations would be much different (lesser) from that of the zones X i and X j with similar masses mX i and mX j but situated at strategically highly significant locations. Based on this argument, we provide a modified gravity model by incorporating the dX ij ≠ dX ji , and the product of location significance indexes (φX i φX j ) of the corresponding zones. This modified gravity model yields the level of interaction between the two zones that satisfies FXij ≠ FXji. We demonstrate this modified gravity model on the 28 states of India, whereby the areal extents (land resources) of each state is considered as a parameter mass. The levels of interactions are presented for all pairs of states.