This is final version. Available on open access from Springer via the DOI in this record.We propose a method for examining and measuring the complexity of animal social networks that are characterized using association indices. The method focusses on the diversity of types of dyadic relationship within the social network. Binomial mixture models cluster dyadic relationships into relationship types, and variation in the preponderance and strength of these relationship types can be used to estimate association complexity using Shannon’s information index. We use simulated data to test the method, and find that models chosen using integrated complete likelihood give estimates of complexity that closely reflect the true complexity of social systems, but these estimates can be downwardly biased by low intensity sampling and upwardly biased by extreme overdispersion within components. We also illustrate the use of the method on two real data sets. The method could be extended for use on interaction rate data using Poisson mixture models, or on multidimensional relationship data using multivariate mixture models
