  Social animals self-organise to create groups to maximise protection against
predators, productivity and fitness. One-to-one interactions are the building
blocks of these emergent social structures and may correspond to friendship,
grooming, communication, among other social relations. These structures should
be robust to failures and provide efficient communication to compensate the
costs of forming and maintaining the social contacts but the specific purpose
of each social interaction regulates the evolution of the respective social
networks. We collate 637 animal social networks and show that the number of
social interactions scales with group size as a super-linear power-law for
various species of animals, including humans, other mammals and non-mammals. We
identified that the super-linear exponents fall in 3 broad classes depending on
the social function, i.e. cooperation, spatial proximity, and friendship. By
fitting a hierarchical model to our data, we observed that social hierarchy
must be absent to create efficient network structures for cooperation. This is
not the case for friendship ties where network performance is not driven by
group survival. Social interactions measured by spatial proximity fall in an
intermediary category, not as efficient as cooperation, and is likely more
relevant for the spread of infectious diseases than for social phenomena.
