We show that several models where electric polarization in molecular systems is modeled by charge-flow between atoms can all be considered as different manifestations of a general underlying mathematical structure. The models can be classified according to whether they employ atomic or bond parameters and whether they employ atom/bond hardness or softness. We show that an ab initio calculated charge response kernel can be considered as the inverse screened Coulombic matrix projected onto the zero-charge subspace, and this may provide a method for deriving charge screening functions to be used in force fields. The analysis suggests that some models contain redundancies, and we argue that a parameterization of charge-flow models in terms of bond softness is preferable as it depends on local quantities and decay to zero upon bond dissociation, while bond hardness depends on global quantities and increases toward infinity upon bond dissociation.