The structure of the contact network between individuals has a profound effect on the transmission of infectious disease. Using a novel technology--proximity sensing radio collars--we described the contact network in a population of Tasmanian devils. This largest surviving marsupial carnivore is threatened by a novel infectious cancer. All devils were connected in a single giant component, which would permit disease to spread throughout the network from any single infected individual. Unlike the contact networks for many human diseases, the degree distribution was not highly aggregated. Nevertheless, the empirically derived networks differed from random networks. Contact networks differed between the mating and non-mating seasons, with more extended male-female associations in the mating season and a greater frequency of female-female associations outside the mating season. Our results suggest that there is limited potential to control the disease by targeting highly connected age or sex classes.