Self-consistent inference formulation of gravity model

The gravity model has been a useful framework to describe macroscopic flow patterns in geographically correlated systems. In the general framework of the gravity model, the flow between two nodes decreases with distance and has been set to be proportional to the suitably defined mass of each node. Despite the frequent successful applications of the gravity model and its alternatives, the existing models certainly possess a serious logical drawback from a theoretical perspective. In particular, the mass in the gravity model has been either assumed to be proportional to the total in- and out-flow of the corresponding node or simply assigned the other node attribute external to the gravity model formulation. In the present work, we propose a general novel framework in which the mass as well as the distance-dependent deterrence function can be computed iteratively in a self-consistent manner within the framework only based on the flow data as input. We validate our suggested methodology in an artificial synthetic flow data to find the near-perfect agreement between the input information and the results from our framework. We also apply our method to the real international trade network data and discuss implications of the results.