Our understanding of how cooperation can arise in a population of selfish individuals has been greatly advanced by theory. More than one approach has been used to explore the effect of population structure. Inclusive fitness theory uses genetic relatedness r to express the role of population structure. Evolutionary graph theory models the evolution of cooperation on network structures and focuses on the number of interacting partners k as a quantity of interest. Here we use empirical data from a hierarchically structured animal contact network to examine the interplay between independent, measurable proxies for these key parameters. We find strong inverse correlations between estimates of r and k over three levels of social organization, suggesting that genetic relatedness and social contact structure capture similar structural information in a real population.