Collective animal movements produce spectacular natural phenomena that arise from simple local interactions among group members. Flocks of homing pigeons, Columba livia, provide a useful model for the study of collective motion and decision making. During homing flights, flock members are forced to resolve potentially divergent navigational preferences in order to stay together and benefit from flying in a group. Recent work has demonstrated that some individuals consistently contribute more to the movement decisions of the flock than others do, thereby generating stable hierarchical leader–follower networks. Yet, what attributes of a flying pigeon reliably predict leadership remains an open question. We examined the flexibility of an individual's hierarchical leadership rank (i.e. its ordinal position when flock members are ranked according to the average time differences with which they lead or follow others) as a function of changes in its navigational knowledge. We manipulated already established hierarchical networks in three different flocks, by providing certain individuals with additional homing experience. We found that such training did not consistenly lead to an increase in birds' leadership ranks, and that, in general, the nature of leader–follower interactions between trained and untrained birds remained unaffected. Thus, leadership hierarchies in pigeon flocks appear resistant to changes in the navigational knowledge of a subset of their members, at least when these changes are relatively small. We discuss the implications of our results in light of the potential benefits of structural stability in decision-making networks.