  Spatial interaction and spatial autocorrelation are two different fields of
geo-spatial analysis, revealing the internal relationship between the two
fields will help to develop the theory and method of geographical analysis.
This paper is devoted to deducing a system of spatial correlation analysis
models from the gravity model by mathematical derivation. The main results are
as follows. First, a set of potential energy measurements are derived from the
gravity model. Second, a pair of correlation equations, including an inner
product equation and an outer product equation, are constructed based on the
quadratic form of potential energy formula. Third, a series of spatial
autocorrelation statistics, including Moran's index and Getis-Ord's index are
derived from the potential energy formula. Fourth, the concept of fractal
dimension is introduced into spatial weight matrix. The observational data of
urban systems are employed to make an empirical analysis, demonstrating the
application procedure of newly derived models. A conclusion can be drawn that
spatial autocorrelation is actually rooted in spatial interaction process, and
an improved methodology of spatial analysis can be developed by integrating
spatial autocorrelation models and gravity model into the same framework.
