A computer algorithm is presented to derive initial velocity rate equation for general enzyme raction mechanisms, including sequential as well as complicated random mechanisms. The method is based on the theory of graph and the theory of prime number. In complicated mechanisms, there are many pathways and hence many cycles. The values of the rate constants are constrained according to the principle of detailed balance: the product of rate constants in the clockwise direction of a cycle must equal to the product of the rate constants in the counter-clockwise direction of the same cycle. An algorithm is presented to derive the appropriate constraint equations. These constraint equations are arranged so that when the rate equation is used for estimating rate constants, the resulting rate constants would satisfy the principle of detailed balance automatically.