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 the
topological representatives of a given free group endomorphism. We prove that each type of
periodic orbit realized by an efficient representative is also realised by any representative
of the same free group endomorphism. Moreover, the number of periodic orbits of a given
type is minimized by the efficient representatives.