We define the type of a periodic orbit of a graph map. We consider the class of ‘train-track’representatives, that is, those graph maps which minimize the topological entropy of thetopological representatives of a given free group endomorphism. We prove that each type ofperiodic orbit realized by an efficient representative is also realised by any representativeof the same free group endomorphism. Moreover, the number of periodic orbits of a giventype is minimized by the efficient representatives.