Terrestrial mammals with differentiated social relationships live in 'semi-closed groups' that occasionally accept new members emigrating from other groups. Bottlenose dolphins (Tursiops sp.) in Shark Bay, Western Australia, exhibit a fission-fusion grouping pattern with strongly differentiated relationships, including nested male alliances. Previous studies failed to detect a group membership 'boundary', suggesting that the dolphins live in an open social network. However, two alternative hypotheses have not been excluded. The community defence model posits that the dolphins live in a large semi-closed 'chimpanzee-like' community defended by males and predicts that a dominant alliance(s) will range over the entire community range. The mating season defence model predicts that alliances will defend mating-season territories or sets of females. Here, both models are tested and rejected: no alliances ranged over the entire community range and alliances showed extensive overlap in mating season ranges and consorted females. The Shark Bay dolphins, therefore, present a combination of traits that is unique among mammals: complex male alliances in an open social network. The open social network of dolphins is linked to their relatively low costs of locomotion. This reveals a surprising and previously unrecognized convergence between adaptations reducing travel costs and complex intergroup-alliance relationships in dolphins, elephants and humans.