Fish are not just simple animals with a short-term memory, say researchers.
The guppy is one of the most popular pet fish in the UK
Guppies have been seen living in complex networks, choosing social partners and remembering them, says a team from Leeds and Bath universities.
These networks are structured and appear to conform to the human theory that everyone knows everyone else, through "six chains of separation".
Biologist Dr Darren Croft found that any two fish in their population could be connected via about two others.
He said: "Understanding the structure of social networks is of extreme importance.
"For example, social network analysis has been used to model the spread of diseases such as HIV in human populations, with diseases that are socially transmitted spreading much faster in networks with 'small world'
"An understanding of the structure of social networks in wild animal populations may allow us to make predictions about the spread of diseases, which may be particularly important for endangered and threatened species."
The findings are published in the Proceedings of the Royal Society of London journal.