We examine the problem of consistency between the kinetic and thermodynamic descriptions of reaction networks. We focus on reaction networks with linearly dependent (but generally kinetically independent) reactions for which only some of the stoichiometric vectors attached to the different reactions are linearly independent. We show that for elementary reactions without constraints preventing the system from approaching equilibrium there are general scaling relations for nonequilibrium rates, one for each linearly dependent reaction. These scaling relations express the ratios of the forward and backward rates of the linearly dependent reactions in terms of products of the ratios of the forward and backward rates of the linearly independent reactions raised to different scaling powers; the scaling powers are elements of the transformation matrix, which relates the linearly dependent stoichiometric vectors to the linearly independent stoichiometric vectors. These relations are valid for any network of elementary reactions without constraints, linear or nonlinear kinetics, far from equilibrium or close to equilibrium. We show that similar scaling relations for the reaction routes exist for networks of nonelementary reactions described by the Horiuti-Temkin theory of reaction routes where the linear dependence of the mechanistic (elementary) reactions is transferred to the overall (route) reactions. However, in this case, the scaling conditions are valid only at the steady state. General relationships between reaction rates of the two levels of description are presented. These relationships are illustrated for a specific complex reaction: radical chlorination of ethylene.