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A general network theory for the molecular motor kinesin is developed that is based on the distinct chemical states of the motor and on recent observations about its mechanical steps. For small concentrations of adenosine diphosphate (ADP), the motor's behavior is governed by the competition of two chemomechanical motor cycles which determine the motor's stall force. A third cycle becomes important for large ADP concentrations. The theory provides a quantitative description for the functional dependencies of different motor properties as observed in single molecule experiments.