Redefining the Attraction Measure, Scaling Exponent and Impedance Function of the Gravity Model

Abstract: The attraction measure, scaling exponent, and impedance function of the gravity model are redefined using the concepts from fractals and spatial complexity. Firstly, the attraction measure of spatial interaction in human systems is defined by the product of traffic inflow and outflow. Based on the new definition, the gravity model originating from the Newtonian analogy is differentiated from Wilson's spatial interaction model deriving from entropy-maximizing principle. Secondly, the scaling exponent of the gravity model based on the inverse distance relationship is revealed to be the ratio of the fractal dimension of networks of cities to that of hierarchies of cities. The value of the scaling exponent is then shown to approach to 2, which corresponds to the value of the power exponent of the law of gravity in classical physics. Thirdly, the inverse power function is demonstrated to be more acceptable than the negative exponential function as an impedance function of the gravity model. The limits of application of different gravity models based on different impedance functions are brought to light. Applying the expanded theory and models to China's interregional flows yields satisfying results, which in turn lend further support to the expanded theory and models.