Abstract: Many group-living animals show social preferences for relatives, familiar conspecifics or individuals of similar attributes such as size, personality or sex. How such preferences could affect the collective motion of animal groups has been rather unexplored. We present a general model of collective animal motion that includes social connections as preferential reactions between individuals. Our conceptual examples illustrate the possible impact of underlying social networks on the collective motion of animals. Our approach shows that the structure of these networks could influence: (1) the cohesion of groups; (2) the spatial position of individuals within groups; and (3) the hierarchical dynamics within such groups. We argue that the position of individuals within a social network and the social network structure of populations could have important fitness implications for individual animals. Counterintuitive results from our conceptual examples show that social structures can result in unexpected group dynamics. This sharpens our understanding of the way in which collective movement can be interpreted as a result of social interactions.