This paper estimates endogenous nodal attractions with exogenous nodal spatial interaction and impedance data with a specific unconstrained gravity model. An algebraic simplification method is developed to use minimum inter-nodal interaction data to derive satisfactory nodal attraction estimates. As applied to a 5x5 origin-destination case, the method can potentially be used for large-scale spatial interaction analyses in which obtaining a complete inter-nodal interaction matrix is impossible or a reduction of computation is necessary.