Biological swarms are collections of many independent agents who are motivated to remain clustered in a large group. The motion of swarms, then, is complex, with the influence if independent members within a coherent structure of the group. We investigated whether human perception of biological swarms was sensitive to this internal complexity of the group motion, as has been observed for biological motion of single objects, such as the limbs of a walking person. In two experiments, we tested motion detection and discrimination of biological swarm motion compared with scrambled, unstructured spiral and rigidly-structured rotational motion. The results showed that discrimination of swarms was superior to perception of scrambled swarms that contained no structure, but was worse than discrimination of the motion of rigid structures. These results suggest that perception of swarms does not engage a specialized mechanism for detecting internal structure, as is found with other types of biological motion, but instead reflects the properties of perception of a coherent global motion. These results have implications for the design of human-machine interfaces. The majority of existing human-robot swarm interaction visualizations presents the human user with each individual swarm member. The presented results imply that an abstract visualization representing the general swarm structure will perform as well, or better than visualizations of each individual.