Techniques recently developed for the analysis of human social networks are applied to the social network of bottlenose dolphins living in Doubtful Sound, New Zealand. We identify communities and subcommunities within the dolphin population and present evidence that sex- and age-related homophily play a role in the formation of clusters of preferred companionship. We also identify brokers who act as links between sub-communities and who appear to be crucial to the social cohesion of the population as a whole. The network is found to be similar to human social networks in some respects but different in some others, such as the level of assortative mixing by degree within the population. This difference elucidates some of the means by which the network forms and evolves.