Dominance hierarchy among animals is widespread in various species and believed to serve to regulate resource allocation within an animal group. Unlike small groups, however, detection and quantification of linear hierarchy in large groups of animals are a difficult task. Here, we analyse aggression-based dominance hierarchies formed by worker ants in Diacamma sp. as large directed networks. We show that the observed dominance networks are perfect or approximate directed acyclic graphs, which are consistent with perfect linear hierarchy. The observed networks are also sparse and random but significantly different from networks generated through thinning of the perfect linear tournament (i.e., all individuals are linearly ranked and dominance relationship exists between every pair of individuals). These results pertain to global structure of the networks, which contrasts with the previous studies inspecting frequencies of different types of triads. In addition, the distribution of the out-degree (i.e., number of workers that the focal worker attacks), not in-degree (i.e., number of workers that attack the focal worker), of each observed network is right-skewed. Those having excessively large out-degrees are located near the top, but not the top, of the hierarchy. We also discuss evolutionary implications of the discovered properties of dominance networks.